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Felipe VI

Felipe VI (Felipe Juan Pablo Alfonso de Todos los Santos de Borbón y Grecia; born 30 January 1968) is King of Spain. In accordance with the Spanish Constitution, as monarch, he is head of state and commander-in-chief of the Spanish Armed Forces, holding the military rank of Captain General, and also plays the role of the supreme representation of Spain in international relations.

Felipe was born in Madrid during the dictatorship of Francisco Franco as the third child and only son of Prince Juan Carlos of Spain and Princess Sophia of Greece and Denmark. Felipe was officially created Prince of Asturias in 1977, two years after his father became king. Felipe was formally proclaimed as prince in 1986. He was also made honorary soldier of the Spanish Army at the age of 9. Felipe was educated at Santa María de los Rosales School and went to Lakefield College School in Canada. Later, he studied law at the Autonomous University of Madrid and he obtained a Master of Science in Foreign Service degree from the School of Foreign Service at Georgetown University in Washington, D.C.

To prepare for his future role as commander-in-chief of the Armed Forces, Felipe joined the Spanish Army in 1985. During the next two years, he completed his military training in the Navy and Air Force. After completing his civil and military studies, he undertook official duties representing his father in different social and institutional events, such as chairing charity foundations or attending inaugurations of Latin American leaders. At one of these events with the press, Felipe met TV news journalist Letizia Ortiz Rocasolano, whom he married in 2004. They have two daughters, Leonor, Princess of Asturias, and Infanta Sofía.

Felipe ascended the throne on 19 June 2014 upon the abdication of his father. His reign has been marked by his dissolution of the Spanish Parliament in 2016 (so that new elections could be called), strong condemnation of the Catalan independence referendum that led to the 2017–18 Spanish constitutional crisis, the COVID-19 pandemic, and moves towards greater transparency in royal affairs. According to a poll conducted in 2020, Felipe has moderately high approval ratings.

Early life and family
Felipe was born at 12:45 (CET) on 30 January 1968, at Our Lady of Loreto Hospital at Madrid, being the third child and only son of Prince Juan Carlos of Spain and Princess Sophia of Greece and Denmark. He was baptized on 8 February 1968 at the Palace of Zarzuela by the Roman Catholic Archbishop of Madrid, Casimiro Morcillo, with water from the Jordan River. His full baptismal name, Felipe Juan Pablo Alfonso de Todos los Santos, consists of the names of the first Bourbon king of Spain (Felipe V), his grandfathers (Infante Juan, Count of Barcelona, and King Paul of Greece), his great-grandfather Alfonso XIII of Spain, and de Todos los Santos ("of all the Saints") as is customary among the Bourbons. His godparents were his paternal grandfather, the Count of Barcelona, and his paternal great-grandmother, Queen Victoria Eugenie. Additionally, he is the third cousin once removed of King Harald V of Norway, Queen Margrethe II of Denmark, and King Carl XVI Gustav of Sweden, and second cousin once removed of King Charles III of the United Kingdom.

Shortly after his birth Felipe was styled infante. The dictator Francisco Franco died just over two months before Felipe's eighth birthday, and Felipe's father ascended the throne, as the latter had been appointed as Prince of Spain back in 1969. In his first official appearance, Felipe attended his father's proclamation as king on 22 November 1975.

Prince of Asturias
In 1977, Felipe was formally proclaimed Prince of Asturias. In May, nine-year-old Felipe was made an honorary soldier of the 1st King's Inmemorial Infantry Regiment. The occasion was marked on 28 May and was attended by the king, the prime minister and several other ministers in a ceremony at the infantry's barracks. On 1 November the same year, he was ceremoniously paid homage as Prince of Asturias in Covadonga. In 1981 Felipe received the Collar of the Order of the Golden Fleece from his father, the Chief and Sovereign of the Order. On his 18th birthday on 30 January 1986, Felipe swore allegiance to the Constitution and to the King in the Spanish Parliament as required by the constitution, fully accepting his role as successor to the Crown.

Education and military training
Felipe attended school at Santa María de los Rosales, which his daughters both attended. Felipe attended high school at Lakefield College School in Ontario, Canada, and studied at the Autonomous University of Madrid, where he graduated with a degree in law; he also completed several courses in economics. He completed his academic studies by obtaining a Master of Science in Foreign Service degree from the School of Foreign Service at Georgetown University in Washington, D.C., where he was the roommate of his cousin, Crown Prince Pavlos of Greece.

As the heir to the throne, a carefully regulated and structured plan was laid out for Felipe's military training. In August 1985, a Royal Decree named Felipe as officer at the General Military Academy in Zaragoza. He began his military training there in September. He completed the first phase of his formation in October. In July 1986, he was promoted to Cadet Ensign. He was also named as Midshipman. In September 1986, he began his naval training at the Naval Military Academy in Marin (Pontevedra), joining the Third Brigade. In January 1987, he continued his naval training on board the training ship Juan Sebastián Elcano.

In July, he was named as Student Ensign at the General Air Academy in Murcia. In September 1987, he began his air force training there where he learned to fly aircraft. In 1989, he was promoted to lieutenant in the Army, ensign in the Navy, and lieutenant in the Air Force. In 1992, he was promoted to captain in the Air Force. In 1993, he was promoted to lieutenant in the Navy and captain in the Infantry of the Army.

Further promotions in 2000 were commandant in the Army, corvette captain in the Navy, and commandant in the Air Force. Promotions in 2009 were lieutenant colonel in the Army, frigate captain in the Navy, and lieutenant colonel in the Air Force.

Since 19 June 2014, after his ascension to the throne, he acquired the rank of Captain General (Commander-in-chief) of all the Spanish armies (Army, Navy and Air Force). During the 2016 Pascua Militar, the Chief of the Defence Staff, Fernando García Sánchez, on behalf of the Armed Forces, gifted the monarch with a personalized command baton, which symbolizes the loyalty of the armies to the king and the command he has over them. The piece, made by some jewelers from León, is made of cherry wood and the tips are adorned with silver pieces.

Felipe speaks Spanish, Catalan, French, English and some Greek.

Participation in the Olympics
Felipe was a member of the Spanish Olympic sailing team at the 1992 Summer Olympics held in Barcelona. Felipe took part in the opening ceremony as the Spanish team's flag bearer. The Spanish crew finished in sixth place in the Soling class and obtained an Olympic diploma. He is an honorary member of the International Soling Association. Both his mother and uncle, King Constantine II of Greece, were on the Greek sailing team at the 1960 Summer Olympics in Rome (his mother as a substitute), and Felipe's father and sister were also Olympic sailors for Spain.

Marriage and children
Felipe's bachelor years were a source of interest to the Spanish press for several years. His name was linked with several eligible women, but only two notable girlfriends: Spanish noblewoman Isabel Sartorius, around 1989 to 1991, daughter of the Marquess of Mariño, who was viewed unfavorably by the Royal Family due to her mother's cocaine addiction, and Norwegian model Eva Sannum, who modeled underwear.

Although there were some engagement rumors in the previous weeks, on 31 October 2003, a TV program called Con T de Tarde announced unexpectedly that the Prince of Asturias was dating Letizia Ortiz Rocasolano, a television journalist who had been married previously. The following day, the Royal Household made official their engagement. According to the Royal House, they met in late 2002. The official hand petition was made on 6 November 2003 at the Royal Palace of El Pardo. Felipe proposed with a 16-carat diamond engagement ring with a white gold trim and gifted her with a pearl and sapphire necklace. Ortiz marked the occasion by giving him white gold and sapphire cufflinks and a classic book, El doncel de don Enrique el doliente by Mariano José de Larra.

The wedding, which was officiated by the archbishop of Madrid and president of the Spanish Episcopal Conference, Antonio María Rouco Varela, took place on the morning of 22 May 2004 in the Almudena Cathedral, with representatives of royal families from all over the world and most heads of state from Latin America present. In Spain alone, the royal wedding was watched by more than 25 million viewers, the most watched television event in the history of Spanish television.

Felipe and Letizia have two daughters: Leonor, Princess of Asturias (born 31 October 2005) and Infanta Sofía (born 29 April 2007). Both were born at Ruber International Hospital in Madrid.

Activities in Spain and abroad
Felipe undertook his constitutional duties as heir to the throne, hosting many official events in Spain and participating in all events of different sectors and aspects of Spanish public life. Since October 1995, Felipe has represented the Crown on a series of official visits to the Spanish regions, starting with Valencia. Felipe has held regular meetings with constitutional bodies and state institutions keeping up-to-date with their activities. He also attends meetings of the various bodies of the General State Administration and of the Autonomous Communities Administrations as required by his national and international constitutional obligations. In particular, he has held meetings with people of his generation who have built successful careers in political, economic, cultural and media circles. As part of his military training, Felipe trained as a military helicopter pilot. On occasions when King Juan Carlos I was unable to attend, Felipe presided over the annual presentation of dispatches to officers and non-commissioned officers in the Armed Forces as well as participating in military exercises held by the three Armed Services. Since January 1996, Felipe has represented Spain at many Latin American presidents' inauguration ceremonies. As Prince, he visited every country in Latin America except Cuba, which he visited as King in 11–14 November 2019. He made over 200 foreign trips in total.

Felipe has also played an active role in promoting Spain's economic, commercial and cultural interests and the Spanish language abroad. He frequently represents Spain at world economic and trade events (e.g. Expotecnia, Expoconsumo, and Expohabitat), and is especially interested in promoting the creation of Centres and University Chairs to advance the study of Spain both historically and in the present-day at major foreign universities.

Following the March 2004 Madrid bombings, Felipe, along with his sisters Elena and Cristina, took part in a public demonstration.

Social activities
In addition to his official activities, Felipe serves as honorary president of several associations and foundations, such as the Codespa Foundation, which finances economic and social development in Ibero-America and other countries, and the Spanish branch of the Association of European Journalists, comprising outstanding communications professionals. Most noteworthy is the Prince of Asturias Foundation, where he presides annually at the international awards ceremony of the highly prestigious Princess of Asturias Awards (formerly the Prince of Asturias Awards).

Felipe was appointed a "UN-Eminent Person" by UN Secretary General Kofi Annan in 2001, during its International Year of Volunteers, and continues to make contributions internationally towards enhancing the importance of voluntary work.

Felipe is a member of the Sons of the American Revolution due to his patriot ancestor Charles III of Spain. Later in 2019, as King, he received the World Peace & Liberty Award from the World Jurist Association at the World Law Congress in Madrid.

Accession
On 2 June 2014, King Juan Carlos announced his intent to abdicate in Felipe's favor. As required by the Constitution of Spain, the Council of Ministers began deliberations the following day on an organic law to give effect to the abdication. The law had to be passed by a majority of all members of the Congress of Deputies, the lower house of the Cortes Generales. According to Jesús Posada, the president of the Congress of Deputies, Felipe could be proclaimed king as early as 18 June. On 4 June, El País of Madrid reported that Felipe would indeed be proclaimed king on 18 June.

Felipe ascended the throne at the stroke of midnight on 19 June; his father had given his sanction to the organic law effecting his abdication just hours earlier. The next morning, after receiving the Captain General's sash from his father (symbolizing the transfer of royal and military power), he was formally sworn in and proclaimed king in a low-key ceremony held in the Cortes. He swore to uphold the Constitution before formally being proclaimed king by Posada. Upon his accession, he became the youngest monarch in Europe, being nine months younger than King Willem-Alexander of the Netherlands. As king, Felipe has fairly extensive reserve powers on paper. He is the guardian of the Constitution and is responsible for ensuring it is obeyed and followed. It was expected that he would follow his father's practice of taking a mostly ceremonial and representative role, acting largely on the advice of the government. He indicated as much in a speech to the Cortes on the day of his enthronement, saying that he would be "a loyal head of state who is ready to listen and understand, warn and advise as well as to defend the public interest at all times". While he is nominally chief executive, he is not politically responsible for exercising his powers. Per the Constitution, his acts are not valid unless countersigned by a minister, who then assumes political responsibility for the act in question.

A poll conducted by El País, however, indicates that a majority of Spaniards wish Felipe would play a greater role in politics, with 75% of the 600 people surveyed stating they would approve if he personally pushed the political parties to reach agreements on national problems. According to an El Mundo newspaper poll, Felipe had a greater approval than his father prior to his reign.

On 23 June 2014, he appointed his private secretary since 1995, Jaime Alfonsín, as Private Secretary to the King. Two days later, he also appointed José Manuel de Zuleta y Alejandro, 14th duke of Abrantes, as Private Secretary to the Queen.

On 18 July, the new king chaired his first meeting of the Council of Ministers.

Household reforms
During his ascension speech, Felipe pledged a "renewed monarchy for a new time". A few days later after this, Felipe and Letizia became the first Spanish monarchs to receive and recognize LGBT organisations at the Palace. Felipe also changed the protocol in order to allow people to take the oath of office without a crucifix or Bible. This did not mean, in any way, a change in his relations with the Catholic Church or religion, in fact, on their first overseas trip as king and queen, Felipe VI and Letizia met Pope Francis in the Apostolic Palace on 30 June 2014. They subsequently met with Cardinal Secretary of State Pietro Parolin and Under-Secretary for Relations with States Antoine Camilleri. The visit followed one by King Juan Carlos I and Queen Sofía on 28 April. The king also established a difference between the royal family and the King's family, leaving his sisters and their descendants outside the royal family and, therefore, not carrying out institutional representation of the Crown (although they do it occasionally). In July 2014, the king banned the royal family from working outside the Royal Household and he established an external audit made by the Office of the Comptroller General of the State.

Following orders from the king, since 1 January 2015, the Spanish royal family cannot accept "expensive gifts" when "they exceed social or courtesy uses". In February 2015, Felipe announced he would cut his annual salary by 20% as a result of the economic recession and hardships continuing to hamper Spain.

In June 2015, Felipe VI stripped his sister, Infanta Cristina, of her royal title of Duchess of Palma de Mallorca, after the tax fraud allegations surrounding her and her husband, Iñaki Urdangarín. While her husband was eventually sentenced to six years in prison, she was acquitted of all charges.

In 2017, the Crown opened for the first time the gardens of the royal family's vacation palace, the Marivent Palace, at the request of the regional government of the Balearic Islands. The public can enjoy the gardens as long as the royal family is not there.

On February 2024, the king appointed a new Private Secretary, diplomat Camilo Villarino, at that time Head of the Cabinet of the High Representative of the Union for Foreign Affairs and Security Policy, Josep Borrell. Villarino replaced Jaime Alfonsín, private secretary to Felipe for almost 30 years, both as prince and king. Alfonsin remains in the Household as private counselor. Likewise, in April 2024 the king appointed a new private secretary to the Queen, State lawyer María Dolores Ocaña Madrid, replacing the duke of Abrantes.

2020 royal finances controversy
On 15 March 2020, following the revelation in The Telegraph that Felipe VI appeared as second beneficiary (after his father) of the Lucum Foundation, the entity on the receiving end of a €65 million donation by Abdullah bin Abdulaziz, King of Saudi Arabia, the Royal Household issued a statement declaring (a) that Felipe VI would renounce any inheritance from his father to which he could be entitled, and (b) that Juan Carlos would lose his public stipend from the part of the General State Budget dedicated to the Royal Household. The renunciation of the inheritance is a mere declaration of intent, since the Spanish Civil Code prevents accepting or rejecting an inheritance until the death of the person who bequeaths takes place. The Royal Household also implied that Felipe VI already had prior knowledge of the Lucum Foundation and his condition as beneficiary of the latter since April 2019.

After this controversy, in April 2022 the Council of Ministers approved a Royal Decree elaborated by the Royal Household that puts the King's house completely under the 2013 Transparency Act and the 2015 Senior Officials Act. This implies, on the one hand, a greater control of the Crown's finances, since the Court of Auditors will be able to audit its accounts; on the other hand, the disclosure of the wealth of the king and of the senior officials of the Household.

On 25 April 2022, in a move towards greater transparency, Felipe VI made public his personal assets for the first time, revealing them to be valued at 2.6 million euros (US$2.8 million). The Spanish royal palace stated that his wealth is in savings, current accounts and securities, as well as art, antiques and jewelry; and that he has no real estate or financial dealings abroad. It also noted that Felipe VI had paid tax on all his financial earnings. This amount makes him one of the least wealthy monarchs in the world, despite previous estimates of his father Juan Carlos I's wealth being estimated between $2–2.3 billion.

Dissolution of Parliament
The elections in 2015 resulted in no party winning enough seats to form a government. No agreements with the different parties were successful. After months of talks with the different party leaders, and with there being no apparent candidate in a position of support in forming a government, the king issued a royal decree dissolving parliament with new elections being called in June. This marked the first time since the transition to democracy that an election was called under Article 99.5 of the Constitution, wherein the initiative for issuing the dissolution of the Cortes belonged to the King and not to the Prime Minister.

After the second elections, some socialist MPs abstained in order to make it easy for the conservative prime minister, Mariano Rajoy, to form a new government. The king swore in the new cabinet on 4 November 2016.

Catalan independence referendum
On 3 October 2017, as huge protest rallies and a general strike took place in Catalonia following the 2017 Catalan independence referendum that was deemed illegal by Spanish authorities, Felipe delivered an unusually strongly worded televised address, watched by more than 12 million people across the country, in which he condemned the actions of the referendum organizers for acting "outside the law", accusing them of "unacceptable disloyalty" and of "eroding the harmony and co-existence within Catalan society itself". He also warned the referendum could put the economy of the entire north-east region of Spain at risk.

Reactions to Felipe's speech were mixed. Party officials from the PP, PSOE and Ciudadanos acclaimed the King's "commitment to legality" and the "defense of the Constitution, the [regional] Statute, the rule of law and the territorial integrity of Spain", whereas leaders from Unidos Podemos and Catalunya en Comú criticized it as "as unworthy as it was irresponsible", paving the way for a harsh intervention of the Catalan autonomy. However, some PSOE leaders were upset that the King had not made any call to understanding or dialogue between the Spanish and Catalan governments.

After the speech, where Felipe ordered the "legitimate powers of the State" to ensure "constitutional order", the Spanish government started the process to apply article 155 of the Constitution, which gives special powers to the central government to intervene in a Spanish region. On 27 October 2017, the Spanish Senate approved government proposal to impose direct rule in the region with the support of conservative and socialist votes. The Spanish government dismissed all Catalan authorities, dissolved the regional parliament and called for early elections in 2017.

Conservative government fall and political instability
In May 2018, the Audiencia Nacional issued a ruling finding the ruling party, People's Party, guilty as beneficiary of some corruption cases. The left-wing opposition, led by socialist Pedro Sánchez, called for a vote of no confidence against the conservative prime minister. The Congress of Deputies approved the motion on 1 June 2018, and the King appointed Sánchez as new prime minister on June 2. The socialist minority government lasted for a year and a half, and fell in February 2019 after the government failed to pass the budget.

Although the Socialists won the April 2019 general election, the political scenario was left wide open. The socialist prime minister refused to agree with the leaders of left-wing populist Podemos, and the King dissolved Parliament. The November general election had the same result as in April, so the prime minister agreed to a coalition. Felipe swore in the new coalition cabinet on 13 January 2020.

COVID-19 pandemic
On 18 March 2020, a widespread cacerolada from the balconies of some cities across Spain took place, in an attempt to counter-program the TV discourse of Felipe VI on the COVID-19 pandemic in that country. The intent was to force Juan Carlos I to donate to public healthcare the €100M he had allegedly obtained through kickbacks from Saudi Arabia, which was ultimately dismissed. Despite the attempt to boycott the speech, it was seen by more than 15 million citizens, making it the most watched speech by a monarch in the history of Spain. In July, he led a memorial paying tribute to victims of the pandemic at the Royal Palace.

In December 2021, Felipe VI warned against virus complacency during the pandemic, stating that "the risk has not disappeared."

In the context of the COVID-19 pandemic, King Felipe had to isolate himself in quarantine for testing positive for coronavirus on several occasions between 2020 and 2022. While he was isolated, Queen Letizia replaced him in those events for which she was constitutionally authorized (awards delivery, lunches, event openings, etc.) but not in those activities tightly related to constitutional responsibilities (such as the working meeting with the president of Bosnia and Herzegovina, Željko Komšić, in 2022, which had to be postponed ).

2023 conservative victories and Sánchez re-election
The coalition government formed in 2020 led to almost a complete legislature of stability, however, in May 2023, local and regional elections were held. The result of these elections could not have been worse for the government; although the Socialist Party held up well, losing just 400,000 votes compared to the 2019 regional and local elections, the parties to its left collapsed and, in many regions and cities, disappeared, causing the Socialists to lose most of its regional and local power. After this disastrous result, the socialist prime minister, Pedro Sánchez, requested the king to dissolve Parliament and call early elections with the aim of "clarifying the [will of the] Spanish people about the political forces that should lead this new phase and the policies to be applied". As happened in the regional and local elections, the People's Party led by Alberto Núñez Feijóo won the election, but he fell short of a majority to form a new conservative government. In general, this was considered a victory for Sánchez, who still had a chance to renew its coalition government.

After meeting with political parties represented in parliament, and after verifying that neither Sánchez nor Núñez Feijóo had a sufficient majority to form a government, on 22 August 2023 the king asked the winner of the elections, Alberto Núñez Feijóo, to form a government. As expected, Núñez Feijóo failed to gather enough support to govern and the Congress of Deputies rejected his candidacy. Following new meetings with political parties on early October, the king nominated acting prime minister Pedro Sánchez. After obtaining the support of Sumar and the pro-independence and regionalist political parties, the Congress of Deputies re-elected Sánchez on 16 November 2023 and the king swore in the new cabinet on 21 November 2023.

10th accession anniversary
In 2024 Felipe marked his 10th anniversary of his accession and, for this occasion, the king renewed his motto: "Servicio, compromiso y deber" (English: "Service, commitment and duty"). As was customary during his reign, it was announced that the events to celebrate this anniversary would be discreet.

The celebrations began in the Royal Palace, when the royal family presided, from the interior balcony of the palace, over the Royal Guard changing. Subsequently, and after greeting the citizens who approached the palace, the king presented the Order of Civil Merit to 19 anonymous citizens, each from a Spanish region, as well as from the autonomous cities of Ceuta and Melilla. This event ended with a lunch for the invited authorities and the recipients. Before the start of lunch, the Princess of Asturias and Infanta Sofía surprised the king with an improvised speech to congratulate him on the anniversary.

In the afternoon, the monarch's daughters visited the Royal Collections Gallery with 40 young people who, at some point, won the contest "What is a King to you?", organized annually by the Royal Household and two private foundations that promotes the monarchy. On this occasion, the monarchs surprised the attendees by attending the event when it was not planned.

To conclude the celebrations, public concerts were held in the Royal Palace, including the violinist Ara Malikian, as well as a projection of images on the façade of the palace attended by the royal family.

Sports
Felipe is a huge fan of sports and has attended hundreds of sports events since 1976, when he accompanied his father to a match between Real Madrid and Atlético de Madrid at the 1976 Copa del Generalísimo final. At the end of the event, when asked by journalist about his favourite team, he said Atlético de Madrid. He is also the club's honorary president since 2003. Besides football, he loves skiing, squash and sailing.

As King of Spain, most of the sports have a tournament in his honor, Copa del Rey (King's Cup), which he normally attends and delivers the trophy to the winner. Also, since the reign of Alfonso XIII (1886–1931), the King exercises high patronage over the sports federations. Most of them hold the title of "royal" granted by the ruling monarch; the latest federation to receive this honor was the Rugby Federation in 2023.

It is also common for him to attend international sporting events in which Spanish clubs or Spanish national teams participate. If he cannot attend, it is common for him to be replaced by a member of the royal family, such as Leonor, Princess of Asturias and Infanta Sofía in the UEFA Women's Euro 2022 or Queen Letizia in the 2023 FIFA Women's World Cup final.

International agenda
Since his proclamation as king on 19 June 2014, Felipe VI has visited,, 57 sovereign countries on four continents, in 123 official visits abroad (The number of countries includes Puerto Rico, which has the status of "Commonwealth of the United States"). The first international trip was to the Vatican City on 30 June 2014, to meet with the Pope. The last one was to Panama City, Panama, on 30 June–1 July 2024, to attend the inauguration of José Raúl Mulino as president of Panama.

Most of his visits have been to European countries (22 countries in 69 visits), followed by American countries (19 countries in 33 visits), Asian (12 countries in 15 visits) and African (4 countries in 5 visits). He has never visited an Oceanian country as a king; as prince of Asturias, he visited Australia and New Zealand in 1990.

Ibero-America
Like his father did, Felipe VI has maintained an important presence and influence in the countries of Latin America, Portugal and Brazil. As King of Spain, he represents Spain in all the Ibero-American Summits, normally calling for the "unity" of the region and the strengthening of relations with Spain and the European Union. In this sense, Spain is also the main contributor to the Ibero-American General Secretariat, headquartered in Madrid. This organization is mainly financed by Spain, with more than 60 per cent of the budget as of 2016. Felipe VI has attended all the summits since he ascended the throne. For the 2021 Ibero-American summit in Andorra la Vella, Felipe became the first Spanish monarch to visit neighbouring Andorra, a principality whose co-prince is the Spanish Bishop of Urgell.

Also, as he did as prince of Asturias, Felipe has kept the tradition of attending the inauguration of Latin American leaders. As of January 2024, he has attended more than 80 presidential inaugurations.

Portugal
During the reign of Felipe VI, good relations between Spain and Portugal have continued. After his visit to the Vatican, Felipe dedicated his second foreign visit to Portugal, in July 2015. There, he met with President Aníbal Cavaco Silva and Prime Minister Pedro Passos Coelho, and stated that the relationship between the two countries was "not only the relationship of good neighbors, but of brother countries" and remembered that his grandfather, Infante Juan, Count of Barcelona, chose Portugal to live while in exile. He also made it clear that he intended to keep the good relationship between the neighbor countries.

After the election of Marcelo Rebelo de Sousa as new president of Portugal, he made his first official visit to a foreign country to Spain in March 2016. The king, who had attended the inauguration of Rebelo de Sousa early that month, and the Portuguese leader, had established a very good relationship, being described as a true friendship. In addition to courtesy and institutional visits, it is very common to see both leaders in each other's countries as well as attending various events led by the other. Examples of this good relationship are the support that the Portuguese president gave to the king when the monarch was awarded with the Peace and Freedom Award from the World Association of Jurists in 2018, the private visit that Rebelo de Sousa made to Spain in 2020 to visit the Prado Museum and having a private lunch with the monarch at Zarzuela Palace, as well as in 2021, when they were seen eating on a public terrace near the Royal Palace of Madrid.

Cuba
From 11 to 14 November 2019, on the occasion of the 500th anniversary of the founding of the city of Havana by the Spanish, Felipe and Letizia made a state visit to Cuba. This was the fifth royal visit to the island after Infanta Eulalia, Duchess of Galliera in 1893, Infante Alfonso, Count of Covadonga in 1937, Infante Juan, Count of Barcelona in 1948 and King Juan Carlos in 1999. However, King Felipe's visit was the first state visit in history. The visit was harshly criticized by the conservative opposition, as well as by the Cuban opposition and human rights associations which considered the visit a legitimization of the regime.

The Spanish monarchs, who were greeted with cheers by the Cubans, were also welcomed by Cuban president Miguel Díaz-Canel and his wife, Lis Cuesta Peraza. After signing some cooperation agreements and receiving the baton of the city, the royal couple walked through the streets of the Cuban capital and visit the most relevant monuments and buildings. The next day, King Felipe awarded Eusebio Leal with the Grand Cross of the Order of Charles III, a relevant Cuban historian who already held the grand crosses of the orders of Alfonso X, the Wise and Isabella the Catholic.

To conclude the trip, the monarchs traveled to Santiago de Cuba and visited the Castillo de San Pedro de la Roca, where they paid homage to the fallen in the Cuban War of Independence (1895–1898) and Spanish–American War of 1898.

Mexico
Felipe has had a good relationship with Mexico, coinciding in his first years of reign with president Enrique Peña Nieto, who favored this relationships. Felipe made a state visit to the North American country in 2015. However, things got worse with the rise to power of Andrés Manuel López Obrador. López Obrador was inaugurated as Mexican president in December 2018, an inauguration attended by the King, and from the beginning, the Mexican president showed rejection of what Spain and its companies represented.

At the beginning of 2019, the Mexican president asked Felipe VI for an apology on behalf of the Crown and of Spain for the events that occurred during the Spanish conquest of the Americas. The Royal Household did not respond to this request, forwarding the letter from the Mexican president to the Government. In a release, the Spanish government "firmly rejected" López Obrador's arguments and encouraged both governments to "work together" to "intensify the already existing relations of friendship and cooperation". This request for an apology and the criticism for not answering has been reiterated by the Mexican president on various occasions between 2020 and 2022.

After this incident, neither the Royal Family nor the King's Household have spoken about the issue or intervened in any way in the relations between Spain and Mexico, leaving it in the hands of the Government.

Gibraltar
As King of Spain, Felipe has defended the historic claim of Spain over Gibraltar. In September 2014, he addressed the United Nations General Assembly for the first time and, although he made some reference to the territorial integrity of the states, he did not directly mentioned Gibraltar.

Two years later, in another speech at the UN General Assembly podium, the king referred to Gibraltar as the "only existing colony in European territory" and he invited the UK to "put an end to this anachronism with a agreed solution between our two countries that restores the territorial integrity of Spain and is beneficial for the population of the colony and Campo de Gibraltar".

The last time the King mentioned the Gibraltar dispute was on his state visit to the United Kingdom.

State trip to the UK
From 12 to 14 July 2017, the King and Queen of Spain made a state visit to the United Kingdom, which had been postponed twice: the first in March 2016, due to the political crisis in Spain and the second in May 2017, due to the advancement of the British elections.

On Wednesday morning the 12th, Charles, Prince of Wales, and Camilla, Duchess of Cornwall, came to receive the King and Queen. From there, they proceeded to Horse Guards Parade, where they were officially received by Queen Elizabeth II and Prince Philip, Duke of Edinburgh, with military honours and ordnance salutes. The hymns of the two countries were played and the King reviewed the Guard formed there. Next, they moved to Buckingham Palace where they visited the Picture Gallery. In the afternoon Felipe went to the Parliament of the United Kingdom where he addressed a few words at the joint session and held an informal meeting with the leader of the Labour opposition, Jeremy Corbyn. During his speech before parliament, he mentioned the status of Gibraltar, saying that "I am certain that this resolve to overcome our differences will be even greater in the case of Gibraltar, and I am confident that through the necessary dialogue and effort our two governments will be able to work towards arrangements that are acceptable to all involved". In the evening, the State Dinner, hosted by Queen Elizabeth and Prince Philip in honor of the King and Queen of Spain, took place in the Gala Hall of Buckingham Palace.

On Thursday the 13th, there was a Spanish-British business meeting (UK-SPAIN Business Forum) at Mansion House, with the presence of the Mayor of the City of London, Andrew Parmley, and an important business delegation from both countries. Later, the party moved to Westminster Abbey accompanied by Prince Harry. There, the King made an offering at the tomb of the unknown soldier. At mid-morning, they went to the Spanish Embassy in London, in which they received representatives of the Spanish community residing in the English capital and where, previously, they had held a brief meeting with the families of Ignacio Echeverría and Aysha Frade, murdered in the terrorist attacks in London. Later, the King moved to 10 Downing Street, where he had a working lunch with the Prime Minister of the United Kingdom, Theresa May, in which they discussed matters of bilateral interest. Thursday's day was completed with a gala dinner offered by the Mayor of London in honor of the King and Queen, at Guildhall.

On Friday the 14th, Felipe and Letizia were officially bid farewell by Elizabeth and Philip, at the gates of Buckingham Palace. Subsequently, Felipe and Letizia moved to the Francis Crick Institute, a biomedical research center that houses the largest individual biomedical laboratory in Europe. Later they went to Oxford to visit the Weston Library, where they were shown a manuscript of the Codex Mendoza, they saw a copy of a Ptolemy, with the coat of arms of the Catholic Monarchs and an original copy of a first edition of Don Quixote. At noon, Oxford University hosted a luncheon in his honour. To conclude, they held a meeting at Exeter College with representatives of the university's academic community, including professors, postgraduate students and doctoral students linked to Spain.

Jews
Felipe, like his father before him, has supported the initiatives of Spanish institutions to normalize relations with the Jewish people and religion. In 1990, he awarded the Sephardic Jews communities with the Prince of Asturias Award.

In December 2015, the King hosted a solemn ceremony in the Royal Palace to celebrate the approval by the Cortes and the subsequent sanction by the Sovereign of the law that granted Spanish nationality to the Sephardic Jews expelled from Spain in 1492 due to the Alhambra Decree. At his speech, Felipe thanked the Sephardic Jews for preserving their language, Ladino, and for teaching their own children "to love this Spanish homeland". He also welcomed them "back home", adding that they had "returned home forever." The Jewish associations thanked the gesture, declaring that they were no longer "Spaniards without a homeland."

In January 2020, the King attended to the Fifth World Holocaust Forum at Jerusalem. Felipe, who holds the title of King of Jerusalem as one of the historic titles of the Spanish crown, was the only international leader to speak at the opening dinner. In his speech, he stated that "there is no room for indifference in the face of racism, xenophobia, hatred and antisemitism" and that "forgetting the Holocaust would be extremely dangerous and an utter disrespect to the memory of the victims."

On 9 October 2023, King Felipe condemned "with all the firmness" the terrorist attacks against Israel, called for "doing everything possible to avoid greater suffering, destruction, hopelessness and the loss of more human lives" and affirmed that Spain "remains faithful to its commitment to peace and stability in the region". Later that month, during the 2023 Princess of Asturias Awards ceremony, Felipe referred to the ongoing conflict asking for unity to resolve it and remembered that in 1994, Israeli prime minister Yitzhak Rabin and Palestinian leader Yasser Arafat received the Prince of Asturias Award for International Cooperation for their "effort to create conditions of peace in the region" after the Madrid Conference of 1991 and the 1994 Oslo I Accord. On 11 January 2024, the King, in a meeting with the diplomatic corps in Spain, again condemned the terrorist attack, called for the release of the hostages and defended the "establishment of the Palestinian State next to Israel" to stop the "cycle of violence".

Titles and styles
Juan Carlos became King in late November 1975, but no title was conferred on Felipe as heir apparent until 1977, when he was created Prince of Asturias, the traditional title normally held by the heir to the Spanish throne. The royal decree granting him this title also entitled him to use "the other historical titles corresponding to the heir of the Crown". Felipe started using the Aragonese title of Prince of Girona publicly on 21 April 1990, during a trip around Aragon, Catalonia and Valencia, becoming the first Bourbon to use this title.

Upon ascending the throne, Felipe assumed the same titles held by his father. If the former Kingdoms of Aragon and Navarre had separate naming styles, he would also be known as Felipe V of Aragon and Felipe VIII of Navarre along with Felipe VI of Castile.

Arms
As heir to the Spanish throne, Felipe's arms were the Spanish coat of arms with a label of three points azure (blue). The first quarter represents Castile, the second León, the third Aragon, and the fourth Navarre; below are the arms of Granada. In the centre, on an inescutcheon, were the ancestral arms of the sovereign House of Bourbon-Anjou. Surrounding the shield was the collar of the Order of the Golden Fleece and surmounting it was the heraldic crown of the heir to the throne, decorated with four half-arches.

Following his accession to the throne, the label on his arms was removed and the crown of the heir was changed to that of the monarch's (eight half-arches instead of four). These arms differ from those of his father's as king, as they omit the Cross of Burgundy, the yoke, and the sheaf of five arrows.

title: Felipe VI


text:
Shoko Asahara

Shoko Asahara (麻原 彰晃), born Chizuo Matsumoto (松本 智津夫), was the founder and leader of the Japanese doomsday cult known as Aum Shinrikyo. He was convicted of masterminding the 1995 sarin gas attack on the Tokyo subway, and was also involved in several other crimes. Asahara was sentenced to death in 2004, and his final appeal failed in 2011. In June 2012, his execution was postponed due to further arrests of Aum members. He was ultimately executed along with other senior members of Aum Shinrikyo on July 6, 2018.

Early life
Chizuo Matsumoto was born on March 2, 1955, the fourth son of a large, poor family of tatami-mat-makers in Kumamoto Prefecture. He had infantile glaucoma from birth, which made him lose all sight in his left eye and go partially blind in his right eye at a young age, and was thus enrolled in a school for the blind when he was 6-years-old due to being unable to follow on the family trade; he never lived with his family again.

Matsumoto discovered a way to earn money by directing other kids to a candy store, and as he was the only student in the school still capable of having some vision, this led to him becoming somewhat well-liked. However, Matsumoto was also known to be a bully at the school, taking advantage of the other students by beating them and extorting money from them. During his adolescence, Matsumoto developed a fantasy about ruling a kingdom of robots with total power and confided in his schoolmates about his aspiration to rule Japan as Prime Minister.

He graduated in 1973 and applied to study politics at Tokyo University, but was rejected. He then turned to the study of acupuncture and traditional Chinese medicine, which were common careers for the blind in Japan, and he established a Chinese medicine shop outside Tokyo. Asahara married the following year and eventually fathered six children, the eldest of whom was born in 1978. In 1981, Matsumoto was convicted of practicing pharmacy without a license and selling unregulated drugs, for which he was fined ¥200,000 (equivalent to about ¥270,000 [£1,500] in 2023).

Matsumoto's interest in religion reportedly started at this time. Having been recently married, he worked to support his large and growing family. He dedicated his free time to the study of various religious concepts, starting with Chinese astrology and Taoism. Later, Asahara practiced Western esotericism, yoga, meditation, esoteric Buddhism, and esoteric Christianity. Matsumoto let his hair and beard grow and adopted the name Shoko Asahara. Shoko meaning "an offering of incense" in Japanese, and Asahara being an aristocratic surname, unlike the plebeian surname Matsumoto.

Starting in 1984, Asahara made several pilgrimages to India, where he met Tenzin Gyatso, the 14th Dalai Lama. Asahara later claimed to his followers that he managed to achieve Enlightenment, met Shiva, and was given a "special mission" to preach "real Buddhism" in Japan. The Dalai Lama later distanced himself from Asahara and said that he had met "a strange Japanese man", but denied having any significant relationship with him. Asahara returned permanently to Japan in 1987 and assumed the title sonshi meaning "guru" before stating that he had mastered meditation to such an extent that he could lift himself with his mind. He promoted this achievement with pamphlets produced by his own publishing company, but outside a few Japanese periodicals with an occult subject, little publicity was achieved.

Establishment
Aleph (アレフ), formerly Aum Shinrikyo (オウム真理教), was founded by Asahara in his one-bedroom apartment in Tokyo's Shibuya ward in 1987, starting off as a yoga and meditation class known as Oumu Shinsen no Kai (オウム神仙の会) and steadily grew in the following years. It gained official status as a religious organization in 1989 and attracted a considerable number of graduates from Japan's elite universities, thus being dubbed a "religion for the elite".

Early activities
Although Aum was considered controversial in Japan, it was not initially associated with serious crimes until Asahara became obsessed with Biblical prophecies. Aum's public relations activities included publishing comics and animated cartoons that attempted to tie its religious ideas to popular anime and manga themes, including space missions, powerful weapons, world conspiracies, and the quest for ultimate truth. Aum published several magazines including Vajrayana Sacca and Enjoy Happiness, adopting a somewhat missionary attitude. Isaac Asimov's science fiction Foundation Trilogy was referenced "depicting as it does an elite group of spiritually evolved scientists forced to go underground during an age of barbarism so as to prepare themselves for the moment...when they will emerge to rebuild civilization". It has been posited that Aum's publications used Christian and Buddhist ideas to impress what he considered to be the more shrewd and educated Japanese who were not attracted to boring, purely traditional sermons.

Advertising and recruitment activities, dubbed the "Aum Salvation plan", included claims of curing physical illnesses with health improvement techniques, realizing life goals by improving intelligence and positive thinking, and concentrating on what was important at the expense of leisure. This was to be accomplished by practicing ancient teachings, accurately translated from original Pali sutras. These efforts resulted in Aum being able to recruit a variety of people ranging from bureaucrats to personnel from the Japanese Self-Defense Forces and the Tokyo Metropolitan Police. Authors David Kaplan and Andrew Marshall, in their 1996 book, The Cult at the End of the World, claim that initiation rituals often involved the use of hallucinogens, such as LSD. Religious practices often involved extremely ascetic practices claimed to be "yoga". These included everything from renunciants being hung upside down to being given shock therapy.

The cult started attracting controversy in the late-1980s with accusations of deception of recruits, holding cult members against their will, forcing members to donate money and murdering a cult member who tried to leave in February 1989. Kaplan and Marshall alleged in their book that Aum was also connected with such activities as extortion. The group, authors report, "commonly took patients into its hospitals and then forced them to pay exorbitant medical bills".

Sakamoto family murder
In October 1989, Tokyo Broadcasting System Television (TBS) taped an interview with 33-year-old Tsutsumi Sakamoto, a lawyer working on a class action lawsuit against Aum Shinrikyo, regarding his anti-Aum efforts. However, the network secretly showed a video of the interview to Aum members without Sakamoto's knowledge, intentionally breaking its protection of sources. Aum officials then pressured TBS to cancel the planned broadcast of the interview. Several days later, on November 3, 1989, several Aum Shinrikyo members, including Hideo Murai, chief scientist, Satoro Hashimoto, a martial arts master, Tomomasa Nakagawa and Kazuaki Okazaki drove to Yokohama, where Sakamoto lived. They carried a pouch with fourteen hypodermic needles and a supply of potassium chloride. According to court testimony provided by the perpetrators later, they planned to use the chemical substance to kidnap Sakamoto from Yokohama's Shinkansen train station, but, contrary to expectations, he did not show up—it was a holiday (Bunka no hi, or "Culture Day"), so he slept in with his family at home.

At 3 a.m. on November 5, the group entered Sakamoto's apartment through an unlocked door. Tsutsumi Sakamoto was struck on the head with a hammer, injected with potassium chloride, and strangled. His 29-year-old wife, Satoko Sakamoto (坂本都子 Sakamoto Satoko) was beaten and injected with potassium chloride. Their 14-month-old infant son Tatsuhiko Sakamoto (坂本竜彦 Sakamoto Tatsuhiko) was injected with the potassium chloride and then his face was covered with a cloth. The family's remains were placed in metal drums and hidden in three separate rural areas in three different prefectures (Tsutsumi in Niigata, Satoko in Toyama, and Tatsuhiko in Nagano) so that in case the bodies were uncovered, police might not link the three incidents. Their bed sheets were burned and the tools were dropped in the ocean. The victims' teeth were smashed to prevent identification. Their bodies were not found until the perpetrators revealed the locations after they were captured in connection with the 1995 Tokyo subway attack. By the time police searched the areas in which the victims were placed, their bodies were reduced to bones.

Matsumoto sarin attack
On the night of June 27, 1994, the cult carried out a chemical weapons attack against civilians when they released sarin in the central Japanese city of Matsumoto, Nagano. When carrying out the attack, Aum Shinrikyo had two goals; to attack three judges who were expected to rule against the cult in a lawsuit concerning a real estate dispute, and to test the efficacy of its sarin—which the cult was manufacturing at one of its facilities—as a weapon of mass murder. Residents of Matsumoto had also angered Asahara by vigorously opposing his plan to set up an office and factory in the city's southern area. Opponents of the plan gathered 140,000 signatures on an anti-Aum petition, equivalent to 70 percent of Matsumoto's population at the time.

Aum's original plan to release the aerosol into the Matsumoto courthouse was altered when the cult members arrived in the city after the courthouse had closed. They decided to instead target a three-story apartment building where the city's judges resided. At 10:40 pm, members of Aum used a converted refrigerator truck to release a cloud of sarin which floated near the home of the judges. The truck's cargo space held "a heating contraption that had been specifically designed to turn" twelve litres of liquid sarin into an aerosol, and fans to diffuse the aerosol into the neighbourhood. At 11:30 pm, Matsumoto police received an urgent report from paramedics that casualties were being transported to hospital. The patients were suffering from darkened vision, eye pain, headaches, nausea, diarrhea, miosis (constricted pupils), and numbness in their hands. Some victims described having seen a fog with a pungent and irritating smell floating by. A total of 274 people were treated. Five dead residents were discovered in their apartments, and two died in hospital immediately after admission. An eighth victim, Sumiko Kono, remained in a coma for fourteen years and died in 2008. The fatalities also included Yutaka Kobayashi, a 23-year-old salaryman, and Mii Yasumoto, a 29-year-old medical school student.

Additional incidents before 1995
The cult is known to have considered assassinations of several individuals critical of the cult, such as the heads of Buddhist sects Soka Gakkai and The Institute for Research in Human Happiness. After cartoonist Yoshinori Kobayashi began satirizing the cult, he was included on Aum's assassination list. An assassination attempt was made on Kobayashi in 1993. In 1991, Aum began to use wiretapping to get NTT uniforms/equipment and created a manual for wiretapping.

In July 1993, cult members sprayed large amounts of liquid containing Bacillus anthracis spores from a cooling tower on the roof of Aum Shinrikyo's Tokyo headquarters. However, their plan to cause an anthrax epidemic failed. The attack resulted in a large number of complaints about bad odors but no infections. At the end of 1993, the cult started secretly manufacturing the nerve agent sarin and later VX. Aum tested its sarin on sheep at Banjawarn Station, a remote pastoral property in Western Australia, killing 29 sheep. Both sarin and VX were then used in several assassinations between 1994 and 1995.

At the end of 1994, the cult broke into the Hiroshima factory of Mitsubishi Heavy Industries, in an attempt to steal technical documents on military weapons such as tanks and artillery. In December 1994 and January 1995, Masami Tsuchiya of Aum Shinrikyo synthesized 100 to 200 grams of VX which was used to attack three people. On December 2, Noboru Mizuno was attacked with syringes containing VX Gas, leaving him in a serious condition. The VX victim, who Asahara had suspected was a spy, was attacked at 7:00 a.m. on December 12, 1994, on the street in Osaka by Tomomitsu Niimi and another Aum member, who sprinkled the nerve agent on his neck. He chased them for about 100 yd before collapsing, dying ten days later without coming out of a deep coma. Doctors in the hospital suspected at the time he had been poisoned with an organophosphate pesticide. But the cause of death was pinned down only after cult members arrested for the subway attack in Tokyo in March 1995 confessed to the killing.

On January 4, Hiroyuki Nagaoka, an important member of the Aum Victims' Society, a civil organization that protested against the sect's activities, was assassinated in the same way. In February 1995, several cult members kidnapped Kiyoshi Kariya, a 69-year-old brother of a member who had escaped, from a Tokyo street and took him to a compound in Kamikuishiki near Mount Fuji, where he was killed. His corpse was destroyed in a microwave-powered incinerator and the remnants disposed of in Lake Kawaguchi. Before Kariya was abducted, he had been receiving threatening phone calls demanding to know the whereabouts of his sister, and he had left a note saying, "If I disappear, I was abducted by Aum Shinrikyo".

Police made plans to simultaneously raid cult facilities across Japan in March 1995. Prosecutors alleged Asahara was tipped off about this and that he ordered the Tokyo subway attack to divert police. Meanwhile, Aum had also attempted to manufacture 1,000 assault rifles, but only completed one. According to the testimony of Kenichi Hirose at the Tokyo District Court in 2000, Asahara wanted the group to be self-sufficient in manufacturing copies of the Soviet Union's main infantry weapon, the AK-74; one rifle was smuggled into Japan, to be studied so that Aum could reverse engineer and mass-produce the AK-74. Police seized AK-74 components and blueprints from a vehicle used by an Aum member on April 6, 1995.

Tokyo subway gas attack, arrests, and further incidents
On the morning of March 20, 1995, Aum members released a binary chemical weapon, most closely chemically similar to sarin, in a coordinated attack on five trains in the Tokyo subway system, killing 13 commuters, seriously injuring 54 and affecting 980 more. Some estimates claim as many as 6,000 people were injured by the sarin. It is difficult to obtain exact numbers since many victims are reluctant to come forward. Prosecutors allege that Asahara was tipped off by an insider about planned police raids on cult facilities and ordered an attack in central Tokyo to divert police attention away from the group. The attack evidently backfired, and police conducted huge simultaneous raids on cult compounds across the country.

Over the next week, the full scale of Aum's activities was revealed for the first time. At the cult's headquarters in Kamikuishiki on the foot of Mount Fuji, police found explosives, chemical weapons, and a Russian Mil Mi-17 military helicopter. While the finding of biological warfare agents such as anthrax and Ebola cultures was reported, those claims now appear to have been widely exaggerated. There were stockpiles of chemicals that could be used for producing enough sarin to kill four million people. On March 30, 1995, Takaji Kunimatsu, chief of the National Police Agency, was shot four times near his house in Tokyo and was seriously wounded. While many suspected Aum involvement in the shooting, the Sankei Shimbun reported that Hiroshi Nakamura is suspected of the crime, but nobody has been charged.

On April 23, 1995, Hideo Murai, the head of Aum's Ministry of Science, was stabbed to death outside the cult's Tokyo headquarters amidst a crowd of about 100 reporters, in front of cameras. The man responsible, a Korean member of Yamaguchi-gumi, was arrested and eventually convicted of the murder. His motive remains unknown. On the evening of May 5, a burning paper bag was discovered in a toilet in Tokyo's busy Shinjuku station. Upon examination it was revealed that it was a hydrogen cyanide device which, had it not been extinguished in time, would have released enough gas into the ventilation system to potentially kill 10,000 commuters. On July 4, several undetonated cyanide devices were found at other locations in the Tokyo subway.

During this time, numerous cult members were arrested for various offenses, but arrests of the most senior members on the charge of the subway gassing had not yet taken place. In June, an individual unrelated to Aum had launched a copycat attack by hijacking All Nippon Airways Flight 857, a Boeing 747 bound for Hakodate from Tokyo. The hijacker claimed to be an Aum member in possession of sarin and plastic explosives, but these claims were ultimately found to be false. Asahara was finally found hiding within a wall of a cult building known as "The 6th Satian" in the Kamikuishiki complex on May 16 and was arrested. On the same day, the cult mailed a parcel bomb to the office of Yukio Aoshima, the governor of Tokyo, blowing off the fingers of his secretary's hand.

After 1995
On June 21, 1995, Asahara acknowledged that in January 1994 he ordered the killing of a sect member, Kotaro Ochida, a pharmacist at an Aum hospital. Ochida, who tried to escape from a sect compound, was held down and strangled by another Aum member who was allegedly told that he too would be killed if he did not strangle Ochida. Fumihiro Joyu, one of the few senior leaders of the group under Asahara who did not face serious charges, became official head of the organization in 1999. Kōki Ishii, a legislator who formed an anti-Aum committee in the National Diet in 1999, was murdered in 2002. At 11:50 p.m. on December 31, 2011, Makoto Hirata surrendered himself to the police and was arrested on suspicion of being involved in the 1995 abduction of Kiyoshi Kariya, a non-member who had died during an Aum kidnapping and interrogation.

Trial and execution
Asahara faced 27 counts of murder in 13 separate indictments. The prosecution argued that Asahara gave orders to attack the Tokyo Subway to "overthrow the government and install himself in the position of Emperor of Japan". Later, during the trial which took more than seven years to conclude, the prosecution forwarded an additional theory that the attacks were ordered to divert police attention away from Aum. The prosecution also accused Asahara of masterminding the Matsumoto incident and the Sakamoto family murder. During the trials, some of the disciples testified against Asahara, and he was found guilty on 13 of 17 charges, including the Sakamoto family murder; four charges were dropped. On February 27, 2004, he was sentenced to death. The trial was called the "trial of the century" by the Japanese media.

The defence appealed against Asahara's sentence on the grounds that he was mentally unfit and psychiatric examinations were undertaken. During much of the trials, Asahara remained silent or only muttered to himself. However, he communicated with the staff at his detention facility, which convinced the examiner that Asahara was maintaining his silence out of free will. Owing to his lawyers' failure to submit the statement of reason for appeal, the Tokyo High Court decided on March 27, 2006, not to grant them leave to appeal. This decision was upheld by the Supreme Court of Japan on September 15, 2006. Two re-trial appeals were declined by the appellate court. In June 2012, Asahara's execution was postponed due to arrests of several fugitive Aum Shinrikyo members.

Asahara was executed by hanging at the Tokyo Detention House on July 6, 2018, along with six other cult members. Relatives of victims said they approved the execution. Asahara's final words, as reported by officials, assigned his remains to his fourth daughter, who was unsympathetic to the cult and stated she planned to dispose of the ashes at sea; this was contested by Asahara's wife, third daughter, and other family members, who were suspected of wanting to enshrine the ashes where believers can honor them. Until 2024, the ashes were still at the Tokyo Detention House.

In 2021, the Supreme Court of Japan ordered Asahara's remains to be released to his second daughter, which was affirmed by the Tokyo District Court in 2024.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Shoko Asahara


text:
Busch Memorial Stadium

Busch Memorial Stadium (Busch Stadium II) was a multi-purpose sports facility in St. Louis, Missouri, that operated for 40 years, from 1966 through 2005. Built as Civic Center Busch Memorial Stadium, its official name was shortened to Busch Stadium in January 1982.

The stadium served as the home of the St. Louis Cardinals National League baseball team for its entire operating existence, while also serving as home to the National Football League's Cardinals team for 22 seasons, from 1966 through 1987, as well as the St. Louis Rams during part of the 1995 season. It opened four days after the last baseball game was played at Sportsman's Park (which had been renamed Busch Stadium in 1953, when Anheuser-Busch bought the team). The St. Louis Stars of the NPSL and later NASL played at the stadium from 1967 to 1974; the team later used the stadium for select matches up through the 1977 season.

The stadium was designed by Sverdrup & Parcel and built by Grün & Bilfinger. Edward Durell Stone designed the roof, a 96-arch "Crown of Arches". The Crown echoed the Gateway Arch, which had been completed only a year before Busch Stadium opened. Otherwise, it was very similar in appearance to other circular multipurpose "cookie-cutter" stadiums built in the 1960s and early 1970s in Atlanta, Cincinnati, and Pittsburgh, all of which were essentially open-air copies of the Houston Astrodome.

Its final event was the sixth game of the 2005 NLCS on October 19. The stadium was demolished by wrecking ball in late 2005 and part of its former footprint is occupied by its replacement stadium—the new Busch Stadium (a.k.a. Busch Stadium III), located just south.

Background
With new stadiums such as the Astrodome and Shea Stadium, St. Louis felt the need to modernize. Many of these stadiums demonstrated modern feats of engineering and architecture, but also demonstrated a transition occurring for the American public at the time—traditional to the cutting edge. At the time of design, the Busch Stadium II was planned to be used for several purposes. The stadium was named Civic Center Busch Memorial Stadium. Just weeks after opening, the new stadium hosted the All-Star Game, followed by a performance by the Beatles. The landmark that distinguishes St. Louis' skyline today, the Gateway Arch, was built across the street. To complement this historic landmark, the new stadium had 96 open arches on its roof. As a testament to the design, Busch was one of the last built in the 1960s to be torn down. After serving the St. Louis Cardinals for 40 seasons, it was torn down in 2005.

Construction
The baseball Cardinals had played at Sportsman's Park since 1920, originally as tenants of the St. Louis Browns of the American League.

The Cardinals had long since passed the Browns as St. Louis' premier team, and chafed at having the Browns as landlords. At least as early as the 1940s, the Cardinals had sought to build their own park. Longtime owner Sam Breadon had set aside $3 million to build a new park. However, he was unable to find any land to do so, and World War II put those plans on hold. By 1947, Breadon faced the prospect of having to pay a heavy tax bill on his stadium fund. Tax lawyer Fred Saigh convinced Breadon to sell him the team, arguing this would save the Cardinals from this stiff tax burden.

When this tax dodge came to light in 1953 following an IRS audit, Saigh was subsequently charged with tax evasion, and pleaded no contest. Facing certain banishment from baseball, he put the team up for sale. Ultimately, Anheuser-Busch bought the Cardinals with the specific goal of keeping them in St. Louis.

However, the Cardinals would have needed a new park in any event. Sportsman's Park had been built in its final form in 1909, and had not aged well. By 1953, even with the rent from the Cardinals, there was not nearly enough revenue to bring the stadium up to code, with city officials even threatening to have it condemned. With this in mind, soon after Anheuser-Busch bought the Cardinals, Browns owner Bill Veeck sold the park to the Cardinals, who heavily renovated the park and renamed it Busch Stadium, while Veeck relocated his team to Baltimore (rebranding it the Orioles).

By the late 1950s, however, the need for a new park could no longer be staved off. Sportsman's Park/Busch Stadium had almost no parking, and the neighborhood around it had gone to seed.

In 1958, Charles Farris, the city's head of development, proposed a new stadium downtown as the core of a plan to revive a 31-block area of the business district. The original design of the stadium called for a baseball-only format, but after the NFL's Chicago Cardinals moved to St. Louis at the end of the 1959 season, becoming known as the football Cardinals in St. Louis, the design was altered to accommodate football as well: the football Cardinals would share Sportsman's Park/Busch Stadium with the baseball Cardinals.

With support from the local Chamber of Commerce, the Civic Center Redevelopment Corporation was established in September 1959, and it was given power of eminent domain, which was used to condemn several areas that were rundown or had gone to seed years before, including the small Chinatown district, the Grand Theater (a historic opera house that had evolved into a burlesque strip club), and various flophouses and abandoned warehouses.

Groundbreaking occurred on May 25, 1964, and construction took just under two years. The plan also included parking garages, a hotel (a Stouffer's hotel), and office buildings. A few years later, it also became the new home of the Spanish Pavilion from the 1964 New York World's Fair.

The stadium opened on May 12, 1966, one month into the baseball season, as Civic Center Busch Memorial Stadium. However, the "Civic Center" part was rarely used, and most people called it simply Busch Memorial Stadium.

Subsequent years
The stadium's grass was replaced with AstroTurf in 1970. St. Louis' notoriously hot summers made it difficult to keep the grass alive, especially when the football Cardinals insisted on practicing on the field during the end of the baseball Cardinals' season. The Cardinals retained a full dirt infield for eight seasons. A removable, sectioned Astroturf surface covered the infield during football season. The infield was converted to sliding pits when the surface was replaced for the 1978 baseball season. With artificial turf, the playing conditions at Busch Stadium were among the hottest in baseball, with temperatures well above the local official readings. Anheuser-Busch (who owned the baseball Cardinals at the time) bought the stadium in 1981 for $53 million and removed the "Memorial" from the stadium's name, becoming simply Busch Stadium; the price included the parking garages. Over the years, the grounds became home to bronze statues of Stan Musial, Enos Slaughter, Dizzy Dean, Rogers Hornsby, Red Schoendienst, Lou Brock, Bob Gibson, James "Cool Papa" Bell, George Sisler, Jack Buck, and Ozzie Smith.

Following Busch's last 1995 event—the Rams' October 22 game before the opening of the now-Dome at America's Center—the Cardinals retrofitted it into a baseball-only stadium. A large section of the upper deck outfield seats was closed, replaced with a hand-operated scoreboard and flags commemorating the Cardinals' retired numbers and World Series championships. The stadium's original natural grass field was restored, and the outfield walls were re-painted green from their original blue.

Demolition
Busch Memorial Stadium was originally slated to be imploded, like most modern-day stadium demolitions, to be able to finish construction on the new stadium in time for the 2006 season. Due to fear of damaging the nearby Stadium MetroLink station, it was decided to tear down the stadium with a wrecking ball, piece-by-piece, over the course of a few weeks.

Demolition of the stadium began at 3:07 p.m. CST on November 7 and was completed shortly after midnight on December 8, 2005.

Part of the footprint of the old stadium is now occupied by the outfield of the current stadium. The Cardinals had planned to build Ballpark Village on the site of the stadium ($320 million for the first phase). It was to consist of boutiques and restaurants, condominium apartments anchored by the new headquarters of Centene Corporation—all to be built in time for the All-Star Game in 2009.

None of the construction had occurred until groundbreaking ceremonies on February 8, 2013, and locals derisively referred to its rain-soaked unfinished status before that date as "Lake DeWitt"—after Cardinal President William DeWitt, Jr. In March 2009, the Cardinals announced the site would be used for a softball field and parking during the game.

Baseball
In its opening year, Busch Stadium hosted the All-Star Game, a 2–1 National League victory in 10 innings, mostly remembered for the humidity and 105 F temperatures. The stadium hosted World Series games in six different seasons:, , , , , and. The Cardinals won the World Series in 1967 and 1982 while playing in the stadium (the seventh game of the 1982 Series was won at Busch). The 1968 and 2004 World Series were clinched in Busch Stadium by visitors: the Detroit Tigers in the seventh game and the Boston Red Sox in a four-game sweep, respectively.

The stadium was also the site of Mark McGwire's historic 62nd home run of the 1998 season that broke Roger Maris' single-season record, and also of McGwire's 70th of that season, for a record which lasted until Barry Bonds surpassed it in 2001. The dimensions in the center and the power alleys had been altered from time to time over the years. Initially, the park was very favorable to pitchers, with spacious outfield dimensions. Consequently, its design (as well as the Astroturf surface) was favorable to the Cardinals' style of play for most of the time from the 1960s through the 1990s, which emphasized good baserunning and extra-base hits. Later changes attempted to make the outfield better balanced between pitching and power hitting.

Before the 1996 season, the stadium was retrofitted to become a baseball-only stadium. Part of the top deck in center field was permanently closed, and in 1997, flags were put in place to honor the team's retired numbers and pennants. Even before then, the stadium had come under less scorn from baseball purists than other cookie-cutter stadiums built during the same era, partly because the "crown of arches" gave it a more traditional look than its cousins and partially because it was alone amongst cookie-cutters in having field-level outfield seating.

The baseball diamond was oriented southeast by east (home to center field); the new stadium is aligned east-northeast, the recommended orientation by MLB.

Football
Busch Stadium was also the home of the St. Louis Cardinals of the National Football League for 22 seasons, from 1966 through 1987.

The stadium was one of, and later the smallest, facilities in the NFL: while the football Cardinals played there, it seated 54,692 people, barely more than the NFL's minimum capacity of 50,000 (mandated in 1970). Various efforts were made to get a new larger stadium or expansion of Busch Stadium, but after these failed, Cardinals owner Bill Bidwill relocated the team to Phoenix, Arizona after the 1987 season.

The football Cardinals never hosted a playoff game during their 28 seasons in St. Louis, while the "Gridbirds" made only three playoff appearances during that stretch, losing on the road against the Minnesota Vikings in 1974, Los Angeles Rams in 1975, and Green Bay Packers in 1982. Despite this lack of success, they won the third place Playoff Bowl after the 1964 season, upsetting Vince Lombardi's Packers 31–24 at the Orange Bowl in Miami.

Busch Stadium was also briefly the home of the St. Louis Rams, who had relocated from Anaheim Stadium in Anaheim, California. Due to completion of their new home stadium, the new and nearby Trans World Dome (later renamed the Dome at America's Center) being delayed, the Rams played the first half of the 1995 season at Busch Stadium: for these four home games, Busch Stadium seated 60,000 people.

The Rams played their last game at Busch Stadium on October 22, while the new indoor venue hosted its first NFL game on November 12, 1995.

Between the Cardinals' 1987 departure and the Rams' 1995 arrival, the stadium hosted two NFL pre-season games: one between the Seattle Seahawks and the New England Patriots in 1989, and one between the New York Jets and the Kansas City Chiefs in 1991.

Soccer
The St. Louis Stars, a professional soccer team, played at Busch Stadium for several years in the 1960s and 1970s. They were initially a member of the National Professional Soccer League for one season in 1967 and moved to the North American Soccer League for their remaining seasons, which they split between Busch Stadium and Francis Field. The team set their record attendance of 32,605 against the New York Cosmos in 1977. The Stars were relocated to Southern California after the 1977 season after being unable to sign a new lease at Busch Stadium.

The stadium also hosted international soccer. It served as the temporary home venue for Trinidad and Tobago in a 1985 CONCACAF Championship match against the United States, who won 2–1 in front of 15,823 fans. The match was part of regional qualifiers for the 1986 FIFA World Cup.

The annual Bronze Boot Game between the Saint Louis Billikens and the SIU Edwardsville Cougars was played at Busch Stadium from 1972 until 1985. The matchup saw record size crowds, including the all-time record attendance for a regular season college soccer match: 22,512 on October 30, 1980.

Concerts
Acts who have performed at Busch Stadium include:
 * The Beatles, on August 21, 1966, during their final North American tour.
 * Jeff Beck, Ted Nugent, Jefferson Starship and Fleetwood Mac, as part of "Super Jam 76"
 * The Rolling Stones, on September 17, 1989, during their Steel Wheels Tour
 * New Kids on the Block on August 26, 1990, during The Magic Summer Tour
 * U2 on September 20, 1992, during their Zoo TV Tour
 * Paul McCartney on April 29, 1993, during The New World Tour
 * Elton John and Billy Joel on August 9, 1994, during their first Face to Face Tour

title: Busch Memorial Stadium


text:
Ingham, Norfolk

Ingham is a small village and civil parish in the English county of Norfolk. It lies close to the village of Stalham, and is about 2 mi from Sea Palling on the North Sea coast.

The civil parish has an area of 1510 acre and in the 2001 census had a population of 376 in 153 households, falling slightly to 374 at the 2011 census. For the purposes of local government, the parish falls within the district of North Norfolk.

There are the remains of a priory and the Ingham Poor's Allotment.

History
Ingham is mentioned in the Domesday Book of 1086 as the village of Hincham in the hundred of Happing. Possible etymologies are "homestead or village of [a man called] Inga" or "home of the Inguiones" (an ancient Germanic tribe).

The Lordship of Ingham was possessed at a very early date by the Ingham family. An Oliver de Ingham was living in 1183 and a John de Ingham is known to have been Lord in the reign of Richard I. The great grandson of John, the distinguished Oliver Ingham lived here and his son-in-law Miles Stapleton of Bedale, Yorkshire, inherited jure uxoris.

Ingham Old Hall has its origins in the medieval times having been built circa 1320. In the 14th century the Hall was inhabited by the local Lord of the Manor, Sir Miles Stapleton, whose tomb stands in Ingham's Holy Trinity church alongside that of his father in law, Sir Oliver de Ingham.

Amenities
The village has one public house, The Ingham Swan, which is one of only two public houses tied to the Woodforde's Brewery of Woodbastwick in Norfolk. The original building was built in the 14th century and was part of Ingham Priory until its destruction under Henry VIII in the 16th century. In spring 2010 chef Daniel Smith and business partner Gregory Adjemian took ownership of the pub, renaming it as The Ingham Swan to avoid confusion with The Swan in nearby Stalham. The building has had much interior renovation.

title: Ingham, Norfolk


text:
Linear classifier

In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class (or group) it belongs to. A linear classifier achieves this by making a classification decision based on the value of a linear combination of the characteristics. An object's characteristics are also known as feature values and are typically presented to the machine in a vector called a feature vector. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use. 5–12–23

Definition

If the input feature vector to the classifier is a real vector $$\vec x$$, then the output score is

 * $$y = f(\vec{w}\cdot\vec{x}) = f\left(\sum_j w_j x_j\right),$$

where $$\vec w $$ is a real vector of weights and f is a function that converts the dot product of the two vectors into the desired output. (In other words, $$\vec{w}$$ is a one-form or linear functional mapping $$\vec x$$ onto R.) The weight vector $$\vec w$$ is learned from a set of labeled training samples. Often f is a threshold function, which maps all values of $$\vec{w}\cdot\vec{x}$$ above a certain threshold to the first class and all other values to the second class; e.g.,

f(\mathbf{x}) = \begin{cases}1 & \text{if }\ \mathbf{w}^T \cdot \mathbf{x} > \theta,\\0 & \text{otherwise}\end{cases} $$

The superscript T indicates the transpose and $$ \theta $$ is a scalar threshold. A more complex f might give the probability that an item belongs to a certain class.

For a two-class classification problem, one can visualize the operation of a linear classifier as splitting a high-dimensional input space with a hyperplane: all points on one side of the hyperplane are classified as "yes", while the others are classified as "no".

A linear classifier is often used in situations where the speed of classification is an issue, since it is often the fastest classifier, especially when $$\vec x$$ is sparse. Also, linear classifiers often work very well when the number of dimensions in $$\vec x$$ is large, as in document classification, where each element in $$\vec x$$ is typically the number of occurrences of a word in a document (see document-term matrix). In such cases, the classifier should be well-regularized.

Generative models vs. discriminative models
There are two broad classes of methods for determining the parameters of a linear classifier $$\vec w$$. They can be generative and discriminative models. Methods of the former model joint probability distribution, whereas methods of the latter model conditional density functions $$P({\rm class}|\vec x)$$. Examples of such algorithms include:
 * Linear Discriminant Analysis (LDA)—assumes Gaussian conditional density models
 * Naive Bayes classifier with multinomial or multivariate Bernoulli event models.

The second set of methods includes discriminative models, which attempt to maximize the quality of the output on a training set. Additional terms in the training cost function can easily perform regularization of the final model. Examples of discriminative training of linear classifiers include:
 * Logistic regression—maximum likelihood estimation of $$\vec w$$ assuming that the observed training set was generated by a binomial model that depends on the output of the classifier.
 * Perceptron—an algorithm that attempts to fix all errors encountered in the training set
 * Fisher's Linear Discriminant Analysis—an algorithm (different than "LDA") that maximizes the ratio of between-class scatter to within-class scatter, without any other assumptions. It is in essence a method of dimensionality reduction for binary classification.
 * Support vector machine—an algorithm that maximizes the margin between the decision hyperplane and the examples in the training set.

Note:  Despite its name, LDA does not belong to the class of discriminative models in this taxonomy. However, its name makes sense when we compare LDA to the other main linear dimensionality reduction algorithm: principal components analysis (PCA). LDA is a supervised learning algorithm that utilizes the labels of the data, while PCA is an unsupervised learning algorithm that ignores the labels. To summarize, the name is a historical artifact.

Discriminative training often yields higher accuracy than modeling the conditional density functions. However, handling missing data is often easier with conditional density models.

All of the linear classifier algorithms listed above can be converted into non-linear algorithms operating on a different input space $$\varphi(\vec x)$$, using the kernel trick.

Discriminative training
Discriminative training of linear classifiers usually proceeds in a supervised way, by means of an optimization algorithm that is given a training set with desired outputs and a loss function that measures the discrepancy between the classifier's outputs and the desired outputs. Thus, the learning algorithm solves an optimization problem of the form

 * $$\underset{\mathbf{w}}{\arg\min} \;R(\mathbf{w}) + C \sum_{i=1}^N L(y_i, \mathbf{w}^\mathsf{T} \mathbf{x}_i)$$

where

 * $w$ is a vector of classifier parameters,
 * $L(y_{i}, w^{T}x_{i})$ is a loss function that measures the discrepancy between the classifier's prediction and the true output $y_{i}$ for the $i$'th training example,
 * $R(w)$ is a regularization function that prevents the parameters from getting too large (causing overfitting), and
 * $C$ is a scalar constant (set by the user of the learning algorithm) that controls the balance between the regularization and the loss function.

Popular loss functions include the hinge loss (for linear SVMs) and the log loss (for linear logistic regression). If the regularization function $R$ is convex, then the above is a convex problem. Many algorithms exist for solving such problems; popular ones for linear classification include (stochastic) gradient descent, L-BFGS, coordinate descent and Newton methods.

title: Linear classifier


text:
Sofía of Spain

Sofía of Spain may refer to:

 * Queen Sofía of Spain (b. 2 November 1938)
 * Infanta Sofía of Spain (b. 29 April 2007)

title: Sofía of Spain


text:
Algebraic integer

In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root of some monic polynomial (a polynomial whose leading coefficient is 1) whose coefficients are integers. The set of all algebraic integers $A$ is closed under addition, subtraction and multiplication and therefore is a commutative subring of the complex numbers.

The ring of integers of a number field $K$, denoted by $\mathcal{O}_{K}$, is the intersection of $K$ and $A$: it can also be characterised as the maximal order of the field $K$. Each algebraic integer belongs to the ring of integers of some number field. A number $α$ is an algebraic integer if and only if the ring $$\mathbb{Z}[\alpha]$$ is finitely generated as an abelian group, which is to say, as a $$\mathbb{Z}$$-module.

Definitions
The following are equivalent definitions of an algebraic integer. Let $K$ be a number field (i.e., a finite extension of $$\mathbb{Q}$$, the field of rational numbers), in other words, $$K = \Q(\theta)$$ for some algebraic number $$\theta \in \Complex$$ by the primitive element theorem.

 * $α ∈ K$ is an algebraic integer if there exists a monic polynomial $$f(x) \in \Z[x]$$ such that $f(α) = 0$.
 * $α ∈ K$ is an algebraic integer if the minimal monic polynomial of $α$ over $$\mathbb{Q}$$ is in $$\Z[x]$$.
 * $α ∈ K$ is an algebraic integer if $$\Z[\alpha]$$ is a finitely generated $$\Z$$-module.
 * $α ∈ K$ is an algebraic integer if there exists a non-zero finitely generated $$\Z$$-submodule $$M \subset \Complex$$ such that $αM ⊆ M$.

Algebraic integers are a special case of integral elements of a ring extension. In particular, an algebraic integer is an integral element of a finite extension $$K / \mathbb{Q}$$.

Examples
1, \alpha, \dfrac{\alpha^2 \pm k^2 \alpha + k^2}{3k} & m \equiv \pm 1 \bmod 9 \\ 1, \alpha, \dfrac{\alpha^2}k & \text{otherwise} \end{cases}$$
 * The only algebraic integers that are found in the set of rational numbers are the integers. In other words, the intersection of $$\mathbb{Q}$$ and $A$ is exactly $$\mathbb{Z}$$. The rational number $a⁄b$ is not an algebraic integer unless $b$ divides $a$. The leading coefficient of the polynomial $bx − a$ is the integer $b$.
 * The square root $$\sqrt{n}$$ of a nonnegative integer $n$ is an algebraic integer, but is irrational unless $n$ is a perfect square.
 * If $d$ is a square-free integer then the extension $$K = \mathbb{Q}(\sqrt{d}\,)$$ is a quadratic field of rational numbers. The ring of algebraic integers $\mathcal{O}_{K}$ contains $$\sqrt{d}$$ since this is a root of the monic polynomial $x^{2} − d$. Moreover, if $d ≡ 1 mod 4$, then the element $\frac{1}{2}(1 + \sqrt{d}\,)$ is also an algebraic integer. It satisfies the polynomial $x^{2} − x + 1⁄4(1 − d)$ where the constant term $1⁄4(1 − d)$ is an integer. The full ring of integers is generated by $$\sqrt{d}$$ or $\frac{1}{2}(1 + \sqrt{d}\,)$  respectively. See Quadratic integer for more.
 * The ring of integers of the field $$F = \Q[\alpha]$$, $3}$, has the following integral basis, writing $m = hk^{2}$ for two square-free coprime integers $h$ and $k$: $$\begin{cases}
 * If $ζ_{n}$ is a primitive $n$th root of unity, then the ring of integers of the cyclotomic field $$\Q(\zeta_n)$$ is precisely $$\Z[\zeta_n]$$.
 * If $α$ is an algebraic integer then $n}$ is another algebraic integer. A polynomial for $β$ is obtained by substituting $x^{n}$ in the polynomial for $α$.

Non-example

 * If $P(x)$ is a primitive polynomial that has integer coefficients but is not monic, and $P$ is irreducible over $$\mathbb{Q}$$, then none of the roots of $P$ are algebraic integers (but are algebraic numbers). Here primitive is used in the sense that the highest common factor of the coefficients of $P$ is 1, which is weaker than requiring the coefficients to be pairwise relatively prime.

Finite generation of ring extension
For any $α$, the ring extension (in the sense that is equivalent to field extension) of the integers by $α$, denoted by $$\Z(\alpha) \equiv \{\sum_{i=0}^n \alpha^i z_i | z_i\in \Z, n\in \Z\}$$, is finitely generated if and only if $α$ is an algebraic integer.

The proof is analogous to that of the corresponding fact regarding algebraic numbers, with $$\Q$$ there replaced by $$\Z$$ here, and the notion of field extension degree replaced by finite generation (using the fact that $$\Z$$ is finitely generated itself); the only required change is that only non-negative powers of $α$ are involved in the proof.

The analogy is possible because both algebraic integers and algebraic numbers are defined as roots of monic polynomials over either $$\Z$$ or $$\Q$$, respectively.

Ring
The sum, difference and product of two algebraic integers is an algebraic integer. In general their quotient is not. Thus the algebraic integers form a ring.

This can be shown analogously to the corresponding proof for algebraic numbers, using the integers $$\Z$$ instead of the rationals $$\Q$$.

One may also construct explicitly the monic polynomial involved, which is generally of higher degree than those of the original algebraic integers, by taking resultants and factoring. For example, if $x^{2} − x − 1 = 0$, $y^{3} − y − 1 = 0$ and $z = xy$, then eliminating $x$ and $y$ from $z − xy = 0$ and the polynomials satisfied by $x$ and $y$ using the resultant gives $z^{6} − 3z^{4} − 4z^{3} + z^{2} + z − 1 = 0$, which is irreducible, and is the monic equation satisfied by the product. (To see that the $xy$ is a root of the $x$-resultant of $z − xy$ and $x^{2} − x − 1$, one might use the fact that the resultant is contained in the ideal generated by its two input polynomials.)

Integral closure
Every root of a monic polynomial whose coefficients are algebraic integers is itself an algebraic integer. In other words, the algebraic integers form a ring that is integrally closed in any of its extensions.

Again, the proof is analogous to the corresponding proof for algebraic numbers being algebraically closed.

Additional facts

 * Any number constructible out of the integers with roots, addition, and multiplication is an algebraic integer; but not all algebraic integers are so constructible: in a naïve sense, most roots of irreducible quintics are not. This is the Abel–Ruffini theorem.
 * The ring of algebraic integers is a Bézout domain, as a consequence of the principal ideal theorem.
 * If the monic polynomial associated with an algebraic integer has constant term 1 or −1, then the reciprocal of that algebraic integer is also an algebraic integer, and each is a unit, an element of the group of units of the ring of algebraic integers.
 * If $x$ is an algebraic number then $a_{n}x$ is an algebraic integer, where $x$ satisfies a polynomial $p(x)$ with integer coefficients and where $a_{n}x^{n}$ is the highest-degree term of $p(x)$. The value $y = a_{n}x$ is an algebraic integer because it is a root of $q(y) = an − 1 n p(y /a_{n})$, where $q(y)$ is a monic polynomial with integer coefficients.
 * If $x$ is an algebraic number then it can be written as the ratio of an algebraic integer to a non-zero algebraic integer. In fact, the denominator can always be chosen to be a positive integer.   The ratio is $|a_{n}|x / |a_{n}|$, where $x$ satisfies a polynomial $p(x)$ with integer coefficients and where $a_{n}x^{n}$ is the highest-degree term of $p(x)$.
 * The only rational algebraic integers are the integers. Thus, if $α$ is an algebraic integers and $$\alpha\in\Q$$, then $$\alpha\in\Z$$. This is a direct result of the rational root theorem for the case of a monic polynomial.

title: Algebraic integer


text:
Millenarianism

Millenarianism or millenarism is the belief by a religious, social, or political group or movement in a coming fundamental transformation of society, after which "all things will be changed". Millenarianism exists in various cultures and religions worldwide, with various interpretations of what constitutes a transformation.

These movements believe in radical changes to society after a major cataclysm or transformative event.

Millenarianist movements can be secular (not espousing a particular religion) or religious in nature, and are therefore not necessarily linked to millennialist movements in Christianity.

Terminology
Both "millennialism" and "millenarianism" refer to "one thousand". They both derive from the Christian tradition. Neither term strictly refers to "one thousand" in modern [1963] academic usage. Millennialism often refers to a specific type of Christian millenarianism, and is sometimes referred to as Chiliasm from the New Testament use of the Greek chilia (thousand).

The terms "millennialism" and "millenarianism" are sometimes used interchangeably, as in The Oxford Handbook of Millennialism. Stephen Jay Gould has argued that this usage is incorrect, stating: "Millennium is from the Latin mille, 'one thousand,' and annus, 'year'—hence the two n's. Millenarian is from the Latin millenarius, 'containing a thousand (of anything),' hence no annus, and only one 'n'."

The application of an apocalyptic timetable to the changing of the world has happened in many cultures and religions, continues to this day, and is not relegated to the sects of major world religions, both Abrahamic and non-Abrahamic. Increasingly in the study of apocalyptic new religious movements, millenarianism is used to refer to a more cataclysmic and destructive arrival of a utopian period as compared to millennialism which is often used to denote a more peaceful arrival and is more closely associated with a one thousand year utopia.

Christian millennialism is part of the broader form of apocalyptic expectation. A core doctrine in some variations of Christian eschatology is the expectation that the Second Coming is very near and that there will be an establishment of a Kingdom of God on Earth. According to an interpretation of biblical prophecies in the Book of Revelation, this Kingdom of God on Earth will last a thousand years (a millennium) or more.

Theology
Many if not most millenarian groups claim that the current society and its rulers are corrupt, unjust, or otherwise wrong, and that they will soon be destroyed by a powerful force. The harmful nature of the status quo is considered intractable without the anticipated dramatic change. Henri Desroche observed that millenarian movements often envisioned three periods in which change might occur. First, the elect members of the movement will be increasingly oppressed, leading to the second period in which the movement resists the oppression. The third period brings about a new utopian age, liberating the members of the movement.

In the modern world, economic rules, perceived immorality or vast conspiracies are seen as generating oppression. Only dramatic events are seen as able to change the world and the change is anticipated to be brought about, or survived, by a group of the devout and dedicated. In most millenarian scenarios, the disaster or battle to come will be followed by a new, purified world in which the believers will be rewarded.

While many millenarian groups are pacifistic, millenarian beliefs have been claimed as causes for people to ignore conventional rules of behaviour, which can result in violence directed inwards (such as the Jonestown mass murder) or outwards (such as the Aum Shinrikyo terrorist acts). It sometimes includes a belief in supernatural powers or predetermined victory. In some cases, millenarians withdraw from society to await the intervention of God. This is also known as world-rejection.

Millenarian ideologies or religious sects sometimes appear in oppressed peoples, with examples such as the 19th-century Ghost Dance movement among Native Americans, early Mormons, and the 19th and 20th-century cargo cults among isolated Pacific Islanders.

The Catechism [doctrine] of the Catholic Church rejects all forms of millenarianism and its variations: "The Antichrist's deception already begins to take shape in the world every time the claim is made to realize within history that messianic hope which can only be realized beyond history through the eschatological judgement. The Church has rejected even modified forms of this falsification of the kingdom to come under the name of millenarianism, especially the 'intrinsically perverse' political form of a secular messianism."

title: Millenarianism