text:
Talk:Hearst Castle

For later use
Art Architectural style Morgan
 * Whitaker, Kathleen. “Art from the Navajo Loom: The William Randolph Hearst Collection.” African Arts 22, no. 2 (February 1989): 98–99.
 *
 * "opulent bordering on (the) delirious".
 *
 * First woman to win AIA Gold Medal, in 2014! LA Times article inaccessible in UK but useful for her bio.
 * Pergola and Zoo - need mentioning in the Estate section.

Xanadu - possible cites

 * https://www.theguardian.com/film/2016/mar/28/scale-of-hearst-plot-to-discredit-orson-welles-and-citizen-kane-revealed
 * https://www.telegraph.co.uk/culture/film/film-news/9033853/Citizen-Kane-feud-between-Orson-Welles-and-William-Randolph-Hearst-thaws-after-70-years.html
 * https://daily.jstor.org/why-william-randolph-hearst-hated-citizen-kane/
 * https://www.history.com/this-day-in-history/william-randolph-hearst-stops-citizen-kane-ads
 * https://books.google.co.uk/books?id=YRic1wGp9bYC&pg=PA20&lpg=PA20&dq=hearst+orson+welles&source=bl&ots=P31o4T9l-w&sig=ACfU3U38pEKZUpslUdK9E2vyjuAsG--49A&hl=en&sa=X&ved=2ahUKEwia0JHD1cPlAhUyUxUIHVk8AWw4MhDoATAFegQICRAB#v=onepage&q=hearst%20orson%20welles&f=false
 * https://books.google.co.uk/books?id=GglIAgAAQBAJ&pg=PA48&lpg=PA48&dq=hearst+orson+welles&source=bl&ots=f1iBWweMRo&sig=ACfU3U322KDn4H95GHucboeXJZlsMBkeUw&hl=en&sa=X&ved=2ahUKEwic0uDE18PlAhX6SxUIHWs-D0k4RhDoATAFegQICBAB#v=onepage&q=hearst%20orson%20welles&f=false

Is Citizen Kane a "satire"?
The film is denoted in the article as a "drama". Can it be, instead, characterized as a "satire"? -The Gnome (talk) 10:43, 24 April 2023 (UTC)

 * RfC background: The status quo in Kane denotes the film as a "drama." In the opening section of the Hearst Castle article, however, the film is denoted as "satire." A dispute arose between another editor and myself on whether the word "satire" is appropriate and sufficient to denote the film. Hence, and after a few reverts, this RfC. -The Gnome (talk) 10:43, 24 April 2023 (UTC)

Comment from KJP1
I'm unsure why The Gnome has chosen to start an RfC here, at Citizen Kane, rather than at Hearst Castle, but I'll post my comments in both for ease.
 * The disagreement between us arose over the use of the word “satirized” in the fourth paragraph of the lead of the Hearst Castle article. The Gnome suggests “evoked” would be more appropriate. My thinking regarding the use of the word goes something like:
 * Multiple RS describe Citizen Kane as a satire, e.g. []
 * They do so because CK does satirize Hearst/Kane, and his wife/mistress Susan/Marion, amongst others. Hearst’s avarice/Davies’ alcoholism are obvious instances. It also accounts for Hearst’s reaction to the film;
 * "Evoking", The Gnome's preferred term, has a rather different, and more benign, meaning;
 * I haven't attempted any major analysis of the film in the Hearst Castle article, but have referenced it in relation to Hearst and his life at the house. I do not understand The Gnome's suggestion that I have sought to "denote" the film as a satire, what I have actually done is say that, in the film, Welles satirises Hearst. I have no wish to alter the coverage of the film given in this article, and have no issue with the description used here, a "drama film";
 * I do note, however, that this article uses the term in question: "The News on the March sequence that begins the film satirizes the journalistic style of The March of Time" (my emphasis);
 * The Gnome appears to take the view that satire is a cheap/debased genre, “merely a satire”. It actually has a long and impressive pedigree, going back to classical texts.

Very pleased of course to discuss and see if a consensus can be reached. Although I would reiterate, I haven't made, and don't propose to make, any change to this article. KJP1 (talk) 11:32, 24 April 2023 (UTC)
 * The obvious reason the talk page of the film Citizen Kane has been chosen for the RfC is that the RfC concerns the nature and assessment of the film - and not the Hearst Castle at all. That's just to respond to the question posed by  KJP1 at the beginning of their comment. For more on my view, I'll be posting here separately. -The Gnome (talk) 18:07, 24 April 2023 (UTC)
 * - I’m afraid I am finding your comments increasingly incomprehensible. We disagreed on one word in the lead to the article on Hearst Castle. You’ve now raised an RfC on this article, Citizen Kane, But I’ve made no comment on, or amendment to this article and don’t intend to. It is not at all “obvious” to me what you are wanting to achieve by this RfC. If it’s an amendment to this article, nothing’s been changed. If it’s an alteration to Hearst Castle, why are we having a discussion here? KJP1 (talk) 20:24, 24 April 2023 (UTC)

Comment from Jack Sebastian
I think that the standard definition of satire, "the use of humor, irony, exaggeration, or ridicule to expose and criticize people's stupidity or vices, particularly in the context of contemporary politics and other topical issues." doesn't really apply to Citizen Kane. I've seen the movie at least a half-dozen times, and I've never found it to be humorous. Now, Charlie Chaplin's The Great Dictator, that's satire pretty much at its finest. CK is a story so told as to not beat you over the head with its metaphors or comparisons to the politics at the time. I think that, as times move on, some of the relevancy to the current events of the time in which the film was made is lost or at the very least, loses some of its satirical (or humorous) value. Maybe its an unfair comparison, but there is more overt satire in Popeye WW2-era cartoons. I can clearly see the satire in Popeye, wielded as it is like a funny hammer. With CK, I see the story, not the satire. That said, that is an opinion that I'm bringing to the discussion here, just as users KJP1 and The Gnome are bringing their own personal interpretations of the definition of satire here. As always, the solution here is going to hinge on the number and quality of Reliable Sources. While the relevancy of sources changes over time (there is a reason why Hedy Lemarr is no longer considered to be the most beautiful woman to appear in film), Wikpedia works because it takes a rather strict stance on the use of sources over personal preference. We have sources that call Citizen Kane satirical, therefore, it is to be noted that it is satire. The reader will decide for themselves if the film is satirical to them. - Jack Sebastian (talk) 13:14, 24 April 2023 (UTC)
 * Very much appreciate the input and it’s helpful to have a range of views. As an aside, this suggests that Welles certainly saw comedic aspects to the film. For me, and I’ve seen it about as many times as you, there are some very humorous aspects to it. And personally, I think it retains a startling relevance, 80-odd years on. Murdoch, Succession, Trump? But you’re right; these are opinions. All the best. KJP1 (talk) 13:39, 24 April 2023 (UTC)

Comment from The Gnome
I've always supported the notion of Wikipedia as reflecting sources rather than arbitrary input. It is an attribute that keeps the project from deteriorating into a ideological battleground, directly and indirectly.

With this clarifying statement out of the way, I should think it'd be obvious that my disagreement about characterizing Citizen Kane as a "satire" is not based in the slightest on my personal opinion on the film, an opinion which I did not divulge at any time. I happen to have read in my time a rather significant amount of literature on film, including film criticism, and thus I happen to be able to recall and invoke sources in support of my disagreement. A task I honestly did not believe I'd ever undertake since there is a veritable avalanche of texts about Kane in which the film's main characteristic is never satire. This is actually close to a "the sky is blue" kind of statement, in the field of film studies, one that's practically self-evident. But there will always be objections, even to the self-evident! Possibly not an altogether bad thing.

KJP1 continues to believe that Kane is satire ("Multiple RS describe Citizen Kane as a satire"). A quick forensics on KJP1's sources actually dispenses rather easily with that belief. What comes off the texts is the fact that the film contains satire but it is far from being a satirical film:

The Sydney Morning Herald review says "Kane is a satire on Hearst himself" but note absence of italics - that's about the character of Kane and not the film. The film, the review, says, is "a journey from innocence to corruption through the ages", "equal parts tragedy and tawdry political opera", "a comedy shot like a horror movie", and so on. (That review is really about the grand lie perpetrated by Pauline Kael, and brought to screen by David Fincher, but Kane gets its share of light.) The Criterion piece contains the word "satire" but, again, the notion is used about the person and not the film ("Kane gives us the definitive satire of a certain American type, it also depicts that type with a fascinating ambivalence, using Freud as much as Marx to understand him"), a film that it describes as "an explosion of form, combining effects and techniques and stylistic flourishes from the preceding decades of film-making (and coming up with several of its own), all in service to an audience-unfriendly downer of a story that offers no uplifting messages or clear moral vision...the peak achievement of Hollywood’s golden age and a rebuke of it — the work of an auteur thumbing his nose at the studio system even as he took full advantage of the resources it provided him". Hardly a satire, this.

What's accessible from the DeGruyter blog has Kane as the "the first American mainstream art film," "a coy  investigation into the life career, and politics of Hearst, and so to dramatize the relations among capitalism, power, sex,  and modern mass media in America." No "satire" in sight. The Columbia Daily Tribune text contains no "satire" either. Catherine Benamou's book Citizen Kane offers us one more text where the author refers to "the perceived cinematic satire of Hearst and his paramour Marion Davies" and goes on to shower t the film itself with major accolades for its artistic and technical achievements, nowhere denoting it as a "satire."

And we come to the infamous Pauline Kael The New Yorker 1971 article on the film. She did not like it. (It is "is closer to comedy than to tragedy". "The mystery in Kane is largely fake". "It isn’t a work of special depth or a work of subtle beauty. It is a shallow work." Etc.) In any case, Kael used the word "satire" in her article twice. The first time to explain why Hollywood became "suspicious" of Welles: "When you write straight reporting about the motion-picture business, you’re writing satire. Motion-picture executives prefer to do business with men whose values they understand. As soon as movies became Welles’ passion, and he was willing to work on any terms, he was finished in the big studios—they didn’t trust him." And the second is to put the film in context in the tradition of vaudevillian comedy: "To use the conventional schoolbook explanations for greatness, and pretend that [the film]'s profound, is to miss what makes it such an American triumph—that it manages to create something aesthetically exciting and durable out of the playfulness of American muckraking satire." Roger Ebert used the word "parody" to denote Welles' use of the concept of the March of Time in Kane. But satire is closely related to but not equal to parody. And Ebert does not make any claim for either "satire" or "parody" for the film itself, in total.

In fact, the only source that has been unearthed claiming straight forwardly that "Kane is primarily a satire" is this personal blog created by a rather unknown "film writer" who writes for the magazine Reverse shot. Should we take this level of obscurity in as evidence? Are even the totality of sources offered strong enough to have us change Kane from drama to satire? I think not. -The Gnome (talk) 22:24, 24 April 2023 (UTC)
 * Setting to one side the fact that I have never suggested we change anything in this article, as it's been dealt with very fully in User:Snow Rise's comments below; you write: "What comes off the texts is the fact that the film contains satire". As you acknowledge this, I'm more puzzled than ever as to the point you are trying to make. If I had written, in this article or elsewhere, something like, "Citizen Kane is a satire and nothing but a satire", you may just about have had a point. But what I wrote was; "Hearst, his castle and his lifestyle were satirized by Orson Welles in his 1941 film Citizen Kane" and you have acknowledged that is exactly what the sources say. And, had your "forensic" been a little less "quick", you'd have seen more instances. You claim, for example, that the Columbia Daily News article "contains no satire". How about the last line of its 15th paragraph: "Welles, in his satire, wanted Hearst to see that his demise was staring at him from the screen"? Or the De Gruyter article: "In its disguised satire of Hearst, Citizen Kane fragments, objectifies, and, so to speak, psychoanalyzes the prototypical biopic subject of the 1930s"? KJP1 (talk) 06:45, 25 April 2023 (UTC)

Yeah, this needs to be moved...
. Sorry, but at least on this procedural issue, you are wrong and is right: if the content issue you are proposing to solve relates to Hearst Castle, and does not involve any suggested or actual change to this article, then this discussion needs to take place on the Hearst Castle talk page. Putting aside the obvious practical reasons an unambiguous status quo of process in this respect, this fact is also expressly covered in policy, such as at WP:TPG, the first sentence of which reads "The purpose of an article's talk page is to provide space for editors to discuss changes to its associated article" and notes under the how to use article talk pages subsection that "Talk pages are for discussing the article, not for general conversation about the article's subject (much less other subjects). Keep discussions focused on how to improve the article." (emphasis in original).

Further, this is more than a purely bureaucratic concern: questions on content and how to form it from sourcing are highly dependent upon context, and hosting this discussion here and being unclear about what change exactly we are addressing highly confuses the relevant editorial issues, complicates any consensus that might result, and would obfuscate the record for anyone addressing the same issue in the future. Unless you believe there are issues impacting this article's discussion of Hearst or any other subject (and it seems obvious from KJP1's comments that no such edits are being contemplated), the appropriate place to have this discussion is on a talk page for an article that actually would be impacted by the discussion.

That said, my opinion of the editorial issue itself (and someone can feel free to ping me to reiterate this if and when the discussion does get moved) is that describing the movie as satire is probably not WP:DUE in the vast majority of cases. Again, context is king, but if I understand the language and location being debated here, it does not seem appropriate. Most but probably not all of the sources KJP1 references above qualify as WP:RS, but of those, only two (or arguably three) actually call the film a satire. The others use the word "satire" in syntactic and semantic forms which do not, in my opinion, directly support labeling the film as such in a fashion which does not require some degree of WP:Synthesis. However, even if all eight sources unambiguously called the film a satire, and all eight were to be regarded as high-quality RS, it would still be a questionable call to use that label, especially in an off-hand reference on an article only tangentially related to the subject, devoid of substantial discussion of the themes of the film. Ultimately this is a matter of WP:WEIGHT: Citizen Kane is one the most heavily discussed films in the history of critical review of the medium, and the vast, vast majority of coverage does not use this label to describe the subject in brief, as the suggested edit on Hearst Castle seems to propose to do.

Now ironically enough, I would actually support some discussion in this article about the role satire may have played in Welles' intentions (short of actually labeling the film "a satire" in Wikivoice) because there does seem to be an agreement in at least a significant number of sources that there was a conscious effort to lampoon Hearst. And if there is ultimately a debate about whether to include such commentary (and what form it should take) in the Citizen Kane article, obviously this would be the place to have that discussion. But placing that descriptor, unqualified, in the lead, would probably not be appropriate, for example. As such, using the label off-hand in a completely different article without that context is even more problematic. Again, please feel free to let me know if the discussion gets relaunched at the Hearst Castle talk page and I will reprise or amend my comments there, as appropriate to that discussion and the precise edits being debated. SnowRise let's rap 06:33, 25 April 2023 (UTC)
 * - Absolutely agree. I did attempt to start the discussion at Talk:Hearst Castle, but User:The Gnome insisted on raising it here. Like you, I'm happy to continue the discussion back at Hearst Castle, should The Gnome choose to relaunch their RfC there. But, as we've already expended quite a lot of ink over one word, and in the interests of collaborative editing, I'd also be very open to changing the single word in dispute. The sentence at Hearst Castle reads: "Hearst, his castle and his lifestyle were satirized by Orson Welles in his 1941 film Citizen Kane." How about replacing "satirized" with, for example; "lampooned" / "caricatured" / "pilloried" / "parodied" / "mocked" / "derided" / "ridiculed"? Other editors will come up with more, and likely better, suggestions. I don't think The Gnome's preference, "evoked", is quite right, as that suggests a more benign intent than Welles had, or than Hearst perceived. KJP1 (talk) 07:13, 25 April 2023 (UTC)
 * Can we know the "intent Welles had"? Well, the next best thing to something written by Welles is Welles speaking his mind about the subject of his film. In this video clip from an interview on the Dick Cavett show, Welles stated unambiguously, "[the character Kane] was not really about him [Hearst]; it was made about a lot of people." Which does not allow for much specific, personal satire of real persons like Hearst. We have a character in the film, Kane, the major character, being presented through a plethora of means and viewpoints, including for sure a satirical perspective of the character and especially the times. And that's all. One-word appellations of the film, or even what Welles did on and about Heart ("his intent") simply do not stand. -The Gnome (talk) 08:01, 25 April 2023 (UTC)
 * If you are seriously suggesting that there are not a wide range of reliable sources which discuss the influence of the real-life Hearst on the character Kane, then your issue is rather wider than the one word we are debating. Take this article which states, "Although various sources were used as a model for Kane, William Randolph Hearst was the primary inspiration". Or this, Sources for Citizen Kane, which quotes Welles; "It's really a quite accurate picture of Hearst to that extent". Or the William Randolph Hearst article itself, which states, "His life story was the main inspiration for Charles Foster Kane". KJP1 (talk) 08:23, 25 April 2023 (UTC)
 * Gnome, please be careful of WP:OR and WP:SYNTH yourself. It doesn't really matter how many quotes from Welles you can provide that you feel support your interpretation of the thematics of his work: if enough secondary WP:reliable sources described the film as a satire of Hearst, we would follow suit.  Getting lost in the weeds of using Welles' own statements for support of this or that take on his intent is not productive under the analysis we utilize on Wikipedia. Sn<b style="color:#99d5fe;">o</b><b style="color:#b2dffe;">w</b><b style="color:#B27EB2;">Rise</b><b style="color:#d4143a"> let's rap</b> 10:00, 25 April 2023 (UTC)
 * KJP1, personally I think all of those terms are probably more problematic from a WP:WEIGHT perspective than the original "satire". However, having looked at the language in the context of the Hearst Castle article, and having done some digging for more sources, I am not absolutely certain that "satirical" as it is used in that article is per se unacceptable.  I do question whether it is WP:DUE enough for the lead of that article, but it is probably an ok way to discuss the ling between Hearst's manor and propensity for acquisition and their fictional parallels in the movie. I say "probably", because it is a nuanced issue that will need more exploration of sourcing to resolve.  However, that is still absolutely and without question, a matter that has to be established by WP:LOCALCONSENSUS on the talk page of that article, where any proposed edits can be discussed in the context of the actual content proposed to be changed and preserved for the record on the correct talk page.  It's not an issue of it "may" be discussed there, nor even that it "should" be.  Under policy, longstanding best practice, and basic editorial common sense, it has to be discussed there. <b style="color:#19a0fd;">S</b><b style="color:#66c0fd">n</b><b style="color:#99d5fe;">o</b><b style="color:#b2dffe;">w</b><b style="color:#B27EB2;">Rise</b><b style="color:#d4143a"> let's rap</b> 10:00, 25 April 2023 (UTC)

 * Thanks for the input, Snow Rise.
 * I agree entirely with your take, which bears repeating here on account of its succinct and strong arguments:
 * "Context is king, but if I understand the language and location being debated here, it does not seem appropriate. Most but probably not all of the sources KJP1 references above qualify as WP:RS, but of those, only two (or arguably three) actually call the film a satire. The others use the word "satire" in syntactic and semantic forms which do not, in my opinion, directly support labeling the film as such in a fashion which does not require some degree of WP:Synthesis. However, even if all eight sources unambiguously called the film a satire, and all eight were to be regarded as high-quality RS, it would still be a questionable call to use that label, especially in an off-hand reference on an article only tangentially related to the subject, devoid of substantial discussion of the themes of the film. Ultimately this is a matter of WP:WEIGHT: Citizen Kane is one the most heavily discussed films in the history of critical review of the medium, and the vast, vast majority of coverage does not use this label to describe the subject in brief, as the suggested edit on Hearst Castle seems to propose to do."
 * Orson Welles himself, not to mention even some of his detractors, could not have put it better!
 * Take care. -The Gnome (talk) 07:31, 25 April 2023 (UTC)

 * P.S. I disagree with your take on this RfC being started here. The RfC simply happened to be triggered by a disagreement in another page. The RfC is about what kind of film is Kane, that is if the film can by summarized in one word, and has nothing to do with the Hearst Castle. In your words: "Placing that ["satire"] descriptor, unqualified, in the lead [of the Hearst Castle article], would probably not be appropriate. ... As such, using the label off-hand in a completely different article without that context is even more problematic." Exactly. We have a major issue on the appellation of Kane itself, an issue concerning the mother article on the film, so to speak, which affects and may affect other articles, in addition to Castle. So, the admonition you quoted ("Keep discussions focused on how to improve the article" e.g. Castle) is of course valid but the Castle article's content is, secondary at best, and used only as the trigger for a wider discussion concerning a different and more important issue. My "Background" introduction could have been omitted and nothing would have changed. In any case, I'll let the discussion proceed here, unless there are many significant arguments against its chosen venue. Cheers. -The Gnome (talk) 07:31, 25 April 2023 (UTC)
 * Nevertheless, both policy and universal practice over the history of this project are crystal clear: we discuss specific proposed changes to the content of articles on the talk pages of those articles. This is WP:NOTAFORUM to discuss the facts relating to the subject in the abstract.  We are only meant to be discussing specific issues relating to changes to the content of the articles, and those discussions are meant to take place on the talk pages connected with those edits, actual or proposed.  There have been no edits to this article resulting from your difference of opinion with KJP1, and no future/speculative edits are proposed either, so there is no policy-consistent discussion to be had here.  The only proposed changes are those you would like to see made at Hearst Castle, and in order to get that done, you must seek a WP:LOCALCONSENSUS on the talk page of that article.  No consensus reached here will be truly binding on that article, and having longwinded debates about what is right for this article when no changes to the status quo are being proposed is just creating walls of text here which serve no purpose, at best, and might even be perceived as WP:disruptive soapboxing. <b style="color:#19a0fd;">S</b><b style="color:#66c0fd">n</b><b style="color:#99d5fe;">o</b><b style="color:#b2dffe;">w</b><b style="color:#B27EB2;">Rise</b><b style="color:#d4143a"> let's rap</b> 10:00, 25 April 2023 (UTC)
 * Understood. I will therefore make no further comment here. Should User:The Gnome start a new/different RfC at Talk:Hearst Castle, we can discuss there. KJP1 (talk) 10:28, 25 April 2023 (UTC)

Restart

 * Transferred here the RfC initially opened at the Kane page. Getting rid of the distraction. -The Gnome (talk) 12:26, 25 April 2023 (UTC)

Observation from KJP1
- I'm really not sure it makes much sense to copy-paste over the original misplaced RfC. Much of that discussion concerned venue, which will make no sense to readers here. Also, the question itself doesn't make much sense. Nowhere in this article is Citizen Kane described as "a satire". The line to which you object reads, "Hearst, his castle and his lifestyle were satirized by Orson Welles in his 1941 film Citizen Kane". I think you'd be better reformulating your RfC to address your specific concern about this wording. Actually, I think you'd be better dropping the stick altogether, and then we have a simple discussion about the word we could use to replace "satirized", but that is your call. KJP1 (talk) 12:55, 25 April 2023 (UTC)
 * The phrase you prefer to denote what Welles created is unacceptable. Welles did not make a "satire" of Hearst Castle. Welles did not even create the character of Kane exclusively based on Hearst. The character, in Welles' own words, was "about many people." These words alone suffice to put the whole matter at rest. (I already provided a source with Welles saying that, and I wish you'd have paid some attention to it rather than insisting you know "what Welles intended," a claim which is pure and personal speculation.) We are bound to paraphrase sources for the sake of avoiding issues of copyright, yes; but our paraphrasing must be neutral.
 * As to your advice about "dropping the stick", it applies to "when the debate has come to a natural end," per that fine essay's text. Do you seriously believe the RfC has come to some kind of an "end," natural or not? Or are you warning me off further participation in the RfC for some reason? -The Gnome (talk) 13:10, 25 April 2023 (UTC)
 * - Actually, I was trying to find a way around your rather battlefield approach. But that clearly isn't going to work, so I shall add my comments below. KJP1 (talk) 13:23, 25 April 2023 (UTC)
 * What would actually be helpful in this discussion is dropping personal acrimony. You now throw a curveball about my "battlefield approach" when nothing I wrote indicates such a frame of mind: Defending one's viewpoint through source-based argumentation, correctly or not, is not doing battle. My suggestion is to assume good faith on my part as I do on yours, and let's proceed to the heart of the matter. Take care. -The Gnome (talk) 13:34, 25 April 2023 (UTC)
 * - I don't think the way you've reproduced the RfC has fired up Requests for comment/Media, the arts, and architecture. KJP1 (talk) 14:26, 25 April 2023 (UTC)
 * And exactly how, pray, is this observation helpful to the discussion? Right after my request to you for a civil discussion, as well. -The Gnome (talk) 16:40, 25 April 2023 (UTC)
 * It informed you of your error, allowing you to correct it and bring this discussion to the attention of a wider audience. Exactly as you did with your earlier, misplaced RfC. KJP1 (talk) 16:59, 25 April 2023 (UTC)

Comments from KJP1
I appreciate User:The Gnome bringing the discussion back here, clearly the right place for debating the wording of this article. I don't fully agree with the wording of the RfC. It is headed "Is Citizen Kane a satire?" and suggests, "In the opening section of the Hearst Castle article, however, the film is denoted as "satire." That isn't strictly accurate. The disputed line, actually a disputed word, reads, "Hearst, his castle and his lifestyle were satirized by Orson Welles in his 1941 film Citizen Kane", i.e. using the film as his vehicle, Welles satirizes Hearst, his home and his life. But, taking the RfC as it stands:
 * There are multiple sources that discuss Welles' use of William Randolph Hearst as a model for Charles Foster Kane in Citizen Kane;
 * There are multiple sources that discuss Welles' use of Hearst Castle as a model for Xanadu;
 * There are multiple sources that discuss Welles' use of Hearst's mania for collecting as a model for Kane's mania for collecting, including Welles himself: "He just acquired things, most of which were never opened, remained in boxes. It's really a quite accurate picture of Hearst to that extent." (Sources for Citizen Kane - Cite 4);
 * All of our existing articles referenced above discuss Welles' use of the Hearst/Hearst Castle models, and other influences, e.g. Marion Davies' alcoholism as a model, at least in Hearst's mind, for the alcoholism of Susan Alexander Kane;
 * I've not reproduced all of the sources which can be found in the articles referenced above;
 * The question is then whether Welles' use of the Hearst-related models can accurately be summarised as "satirizing" them? Again, there are multiple sources which do describe Welles' approach in that way. A sample could include:. It would be possible to find dozens of others through a simple search;
 * I chose to use the word "satirized" for the reasons above, and believe it accurately reflects the sources;
 * I have previously indicated that I should be pleased to discuss the use of an alternative wording and have made a range of possible suggestions above, which I repeat here for ease: "lampooned" / "caricatured" / "pilloried" / "parodied" / "mocked" / "derided" / "ridiculed". I'm not actually sure any are an improvement on "satirized" but would be delighted to discuss them, or other alternatives;
 * I do not agree that User:The Gnome's preferred wording, "evoked", is appropriate. That suggests Welles intended a benign, or at least neutral, portrayal of Kane, and I don't believe it would be supported by the sources. That said, if there are sources of which I'm unaware that do suggest this, we can obviously consider them;
 * For completeness, I've not made any changes to the Citizen Kane article, e.g. changing its lead to describe it as a "satire" rather than a "drama film", and don't intend to.

My apologies for adding further to what has become a rather daunting wall of text. KJP1 (talk) 14:16, 25 April 2023 (UTC)
 * The current text is absolutely fine. Hard to believe this wall of text! Johnbod (talk) 14:31, 25 April 2023 (UTC)
 * Goodness, what a lot of time and effort on this. Reading through the arguments above, looking at the various sources raised by both sides of the debate and doing some further digging into various sources, it's fairly clear the original wording is amply supported by the sources and absolutely fine. I'm not sure why we need—in this article—to include one of the several definitions that can be applied to the film. Yes, it's a drama, but it's also a satire. In her study of Citizen Kane, the film critic Pauline Kael described is as an "American muckraking satire" that is "closer to comedy than to tragedy, though so overwrought in style as to be almost a Gothic comedy". For the phrasing here that is sufficient; I'm not sure why the extended brouhaha over a term that is so amply supported by the sources, but there we go. - SchroCat (talk) 17:55, 25 April 2023 (UTC)

 * I have run across many a fuss about nothing in Wikipedia talk pages, but this one is among the front runners. Let us leave KJP's text as it is: there is not the smallest need for a change.  Tim riley  talk   20:45, 25 April 2023 (UTC)
 * Hear, hear. There is nothing to fix from KJP1's edit. Binksternet (talk) 21:32, 25 April 2023 (UTC)

 * Support for "satire" - Really can't be bothered to climb this wall of text. Having several tragic moments as would a drama, "Citizen Kane" clearly is a satire on Hearst's and similar robber baron's lifestyles making it highly relevlant for our times. 89.206.112.12 (talk) 18:45, 28 April 2023 (UTC)

DYK
It’s germane to this discussion to note that the article has spent much of today on the front page as the lead DYK. In that time it generated no commentary at all, including on the wording of the lead. KJP1 (talk) 14:18, 27 April 2023 (UTC)

Julian Mesic
KJP1 (talk) 06:42, 1 November 2023 (UTC)

title: Talk:Hearst Castle


text:
Optical engineering

Optical engineering is the field of engineering encompassing the physical phenomena and technologies associated with the generation, transmission, manipulation, detection, and utilization of light. Optical engineers use the science of optics to solve problems and to design and build devices that make light do something useful. They design and operate optical equipment that uses the properties of light using physics and chemistry, such as lenses, microscopes, telescopes, lasers, sensors, fiber-optic communication systems and optical disc systems (e.g. CD, DVD).

Optical engineering metrology uses optical methods to measure either micro-vibrations with instruments like the laser speckle interferometer, or properties of masses with instruments that measure refraction.

Nano-measuring and nano-positioning machines are devices designed by optical engineers. These machines, for example microphotolithographic steppers, have nanometer precision, and consequently are used in the fabrication of goods at this scale.

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

title: Optical engineering


text:
Schur complement

The Schur complement of a block matrix, encountered in linear algebra and the theory of matrices, is defined as follows.

Suppose p, q are nonnegative integers such that p + q > 0, and suppose A, B, C, D are respectively p × p, p × q, q × p, and q × q matrices of complex numbers. Let $$M = \left[\begin{matrix} A & B \\ C & D \end{matrix}\right]$$ so that M is a (p + q) × (p + q) matrix.

If D is invertible, then the Schur complement of the block D of the matrix M is the p × p matrix defined by $$M/D := A - BD^{-1}C.$$ If A is invertible, the Schur complement of the block A of the matrix M is the q × q matrix defined by $$M/A := D - CA^{-1}B.$$ In the case that A or D is singular, substituting a generalized inverse for the inverses on M/A and M/D yields the generalized Schur complement.

The Schur complement is named after Issai Schur who used it to prove Schur's lemma, although it had been used previously. Emilie Virginia Haynsworth was the first to call it the Schur complement. The Schur complement is a key tool in the fields of numerical analysis, statistics, and matrix analysis. The Schur complement is sometimes referred to as the Feshbach map after a physicist Herman Feshbach.

Background
The Schur complement arises when performing a block Gaussian elimination on the matrix M. In order to eliminate the elements below the block diagonal, one multiplies the matrix M by a block lower triangular matrix on the right as follows: $$\begin{align} &M = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \quad \to \quad \begin{bmatrix} A & B \\ C & D \end{bmatrix} \begin{bmatrix} I_p & 0 \\ -D^{-1}C & I_q \end{bmatrix} = \begin{bmatrix} A - BD^{-1}C & B \\ 0 & D \end{bmatrix}, \end{align}$$ where Ip denotes a p×p identity matrix. As a result, the Schur complement $$M/D = A - BD^{-1}C$$ appears in the upper-left p×p block.

Continuing the elimination process beyond this point (i.e., performing a block Gauss–Jordan elimination), $$\begin{align} &\begin{bmatrix} A - BD^{-1}C & B \\ 0 & D \end{bmatrix} \quad \to \quad \begin{bmatrix} I_p & -BD^{-1} \\ 0 & I_q \end{bmatrix} \begin{bmatrix} A - BD^{-1}C & B \\ 0 & D \end{bmatrix} = \begin{bmatrix} A - BD^{-1}C & 0 \\ 0 & D \end{bmatrix}, \end{align}$$ leads to an LDU decomposition of M, which reads $$\begin{align} M &= \begin{bmatrix} A & B \\ C & D \end{bmatrix} = \begin{bmatrix} I_p & BD^{-1} \\ 0 & I_q \end{bmatrix}\begin{bmatrix} A - BD^{-1}C & 0 \\ 0 & D \end{bmatrix}\begin{bmatrix} I_p & 0 \\ D^{-1}C & I_q \end{bmatrix}. \end{align}$$ Thus, the inverse of M may be expressed involving D−1 and the inverse of Schur's complement, assuming it exists, as $$\begin{align} M^{-1} = \begin{bmatrix} A & B \\ C & D \end{bmatrix}^{-1} ={} &\left(\begin{bmatrix} I_p & BD^{-1} \\ 0 & I_q \end{bmatrix}        \begin{bmatrix} A - BD^{-1}C & 0 \\ 0 & D \end{bmatrix}         \begin{bmatrix} I_p & 0 \\ D^{-1}C & I_q \end{bmatrix}       \right)^{-1} \\ ={} &\begin{bmatrix}                           I_p & 0 \\ -D^{-1}C & I_q    \end{bmatrix} \begin{bmatrix} \left(A - BD^{-1}C\right)^{-1} & 0 \\       0 & D^{-1} \end{bmatrix} \begin{bmatrix} I_p & -BD^{-1} \\ 0 & I_q \end{bmatrix} \\[4pt] ={} &\begin{bmatrix} \left(A - BD^{-1}C\right)^{-1}       & -\left(A - BD^{-1}C\right)^{-1} BD^{-1} \\ -D^{-1}C\left(A - BD^{-1}C\right)^{-1} & D^{-1} + D^{-1}C\left(A - BD^{-1}C\right)^{-1}BD^{-1} \end{bmatrix} \\[4pt] ={} &\begin{bmatrix} \left(M/D\right)^{-1}       & -\left(M/D\right)^{-1} B D^{-1} \\ -D^{-1}C\left(M/D\right)^{-1} & D^{-1} + D^{-1}C\left(M/D\right)^{-1} B D^{-1} \end{bmatrix}. \end{align}$$ The above relationship comes from the elimination operations that involve D−1 and M/D. An equivalent derivation can be done with the roles of A and D interchanged. By equating the expressions for M−1 obtained in these two different ways, one can establish the matrix inversion lemma, which relates the two Schur complements of M: M/D and M/A (see "Derivation from LDU decomposition" in ).

Properties

 * If p and q are both 1 (i.e., A, B, C and D are all scalars), we get the familiar formula for the inverse of a 2-by-2 matrix:
 * $$ M^{-1} = \frac{1}{AD-BC} \left[ \begin{matrix} D & -B \\ -C & A \end{matrix}\right] $$
 * provided that AD − BC is non-zero.

 * In general, if A is invertible, then
 * $$\begin{align}

M &= \begin{bmatrix} A&B\\C&D \end{bmatrix} = \begin{bmatrix} I_p & 0 \\ CA^{-1} & I_q \end{bmatrix}\begin{bmatrix} A & 0 \\ 0 & D - CA^{-1}B \end{bmatrix}\begin{bmatrix} I_p & A^{-1}B \\ 0 & I_q \end{bmatrix}, \\[4pt] M^{-1} &= \begin{bmatrix} A^{-1} + A^{-1} B (M/A)^{-1} C A^{-1} & - A^{-1} B (M/A)^{-1} \\ - (M/A)^{-1} CA^{-1} & (M/A)^{-1} \end{bmatrix} \end{align}$$
 * whenever this inverse exists.

 * (Schur's formula) When A, respectively D, is invertible, the determinant of M is also clearly seen to be given by
 * $$\det(M) = \det(A) \det\left(D - CA^{-1} B\right)$$, respectively
 * $$\det(M) = \det(D) \det\left(A - BD^{-1} C\right)$$,
 * which generalizes the determinant formula for 2 × 2 matrices.

 * (Guttman rank additivity formula) If D is invertible, then the rank of M is given by
 * $$ \operatorname{rank}(M) = \operatorname{rank}(D) + \operatorname{rank}\left(A - BD^{-1} C\right)$$

 * (Haynsworth inertia additivity formula) If A is invertible, then the inertia of the block matrix M is equal to the inertia of A plus the inertia of M/A.
 * (Quotient identity) $$A/B = ((A/C)/(B/C))$$.
 * The Schur complement of a Laplacian matrix is also a Laplacian matrix.

Application to solving linear equations
The Schur complement arises naturally in solving a system of linear equations such as

$$ \begin{bmatrix} A & B \\ C & D \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} u \\ v \end{bmatrix} $$.

Assuming that the submatrix $$A$$ is invertible, we can eliminate $$x$$ from the equations, as follows.

$$x = A^{-1} (u - By).$$

Substituting this expression into the second equation yields
 * $$\left(D - CA^{-1}B\right)y = v-CA^{-1}u.$$

We refer to this as the reduced equation obtained by eliminating $$x$$ from the original equation. The matrix appearing in the reduced equation is called the Schur complement of the first block $$A$$ in $$M$$:
 * $$S \ \overset{\underset{\mathrm{def}}{}}{=}\ D - CA^{-1}B$$.

Solving the reduced equation, we obtain
 * $$y = S^{-1} \left(v-CA^{-1}u\right).$$

Substituting this into the first equation yields
 * $$x = \left(A^{-1} + A^{-1} B S^{-1} C A^{-1}\right) u - A^{-1} B S^{-1} v. $$

We can express the above two equation as:
 * $$\begin{bmatrix} x \\ y \end{bmatrix} =

\begin{bmatrix} A^{-1} + A^{-1} B S^{-1} C A^{-1} & -A^{-1} B S^{-1} \\ -S^{-1} C A^{-1} &          S^{-1} \end{bmatrix} \begin{bmatrix} u \\ v \end{bmatrix}. $$

Therefore, a formulation for the inverse of a block matrix is:

\begin{bmatrix} A & B \\ C & D \end{bmatrix}^{-1} = \begin{bmatrix} A^{-1} + A^{-1} B S^{-1} C A^{-1} & - A^{-1} B S^{-1} \\ -S^{-1} C A^{-1} &           S^{-1} \end{bmatrix} = \begin{bmatrix} I_p  &  -A^{-1}B\\ & I_q \end{bmatrix}\begin{bmatrix} A^{-1} &  \\ &           S^{-1} \end{bmatrix}\begin{bmatrix} I_p       &  \\ -CA^{-1} & I_q \end{bmatrix}. $$

In particular, we see that the Schur complement is the inverse of the $$2,2$$ block entry of the inverse of $$M$$.

In practice, one needs $$A$$ to be well-conditioned in order for this algorithm to be numerically accurate.

This method is useful in electrical engineering to reduce the dimension of a network's equations. It is especially useful when element(s) of the output vector are zero. For example, when $$u$$ or $$v$$ is zero, we can eliminate the associated rows of the coefficient matrix without any changes to the rest of the output vector. If $$v$$ is null then the above equation for $$x$$ reduces to $$x = \left(A^{-1} + A^{-1} B S^{-1} C A^{-1}\right) u$$, thus reducing the dimension of the coefficient matrix while leaving $$u$$ unmodified. This is used to advantage in electrical engineering where it is referred to as node elimination or Kron reduction.

Applications to probability theory and statistics
Suppose the random column vectors X, Y live in Rn and Rm respectively, and the vector (X, Y) in Rn + m has a multivariate normal distribution whose covariance is the symmetric positive-definite matrix

 * $$\Sigma = \left[\begin{matrix} A & B \\ B^\mathrm{T} & C\end{matrix}\right],$$

where $A \in \mathbb{R}^{n \times n}$  is the covariance matrix of X, $C \in \mathbb{R}^{m \times m}$  is the covariance matrix of Y and $B \in \mathbb{R}^{n \times m}$   is the covariance matrix between X and Y.

Then the conditional covariance of X given Y is the Schur complement of C in $\Sigma$ :

 * $$\begin{align}

\operatorname{Cov}(X \mid Y) &= A - BC^{-1}B^\mathrm{T} \\ \operatorname{E}(X \mid Y) &= \operatorname{E}(X) + BC^{-1}(Y - \operatorname{E}(Y)) \end{align}$$

If we take the matrix $$\Sigma$$ above to be, not a covariance of a random vector, but a sample covariance, then it may have a Wishart distribution. In that case, the Schur complement of C in $$\Sigma$$ also has a Wishart distribution.

Conditions for positive definiteness and semi-definiteness
Let X be a symmetric matrix of real numbers given by $$X = \left[\begin{matrix} A & B \\ B^\mathrm{T} & C\end{matrix}\right].$$ Then
 * If A is invertible, then X is positive definite if and only if A and its complement X/A are both positive definite:
 * $$X \succ 0 \Leftrightarrow  A \succ  0, X/A = C - B^\mathrm{T} A^{-1} B \succ  0.$$

 * If C is invertible, then X is positive definite if and only if C and its complement X/C are both positive definite:
 * $$X \succ 0 \Leftrightarrow C \succ  0, X/C = A - B C^{-1} B^\mathrm{T} \succ  0.$$

 * If A is positive definite, then X is positive semi-definite if and only if the complement X/A is positive semi-definite:
 * $$\text{If } A \succ 0, \text{ then } X \succeq 0 \Leftrightarrow X/A = C - B^\mathrm{T} A^{-1} B \succeq 0.$$

 * If C is positive definite, then X is positive semi-definite if and only if the complement X/C is positive semi-definite:
 * $$\text{If } C \succ 0,\text{ then } X \succeq 0 \Leftrightarrow X/C = A - B C^{-1} B^\mathrm{T} \succeq 0.$$

The first and third statements can be derived by considering the minimizer of the quantity $$u^\mathrm{T} A u + 2 v^\mathrm{T} B^\mathrm{T} u + v^\mathrm{T} C v, \,$$ as a function of v (for fixed u).

Furthermore, since $$                     \left[\begin{matrix} A & B \\ B^\mathrm{T} & C \end{matrix}\right] \succ 0 \Longleftrightarrow \left[\begin{matrix} C & B^\mathrm{T} \\ B & A \end{matrix}\right] \succ 0 $$ and similarly for positive semi-definite matrices, the second (respectively fourth) statement is immediate from the first (resp. third) statement.

There is also a sufficient and necessary condition for the positive semi-definiteness of X in terms of a generalized Schur complement. Precisely,
 * $$X \succeq 0 \Leftrightarrow A \succeq 0, C - B^\mathrm{T} A^g B \succeq 0, \left(I - A A^{g}\right)B = 0 \, $$ and
 * $$X \succeq 0 \Leftrightarrow C \succeq 0, A - B C^g B^\mathrm{T} \succeq  0, \left(I - C C^g\right)B^\mathrm{T} = 0, $$

where $$A^g$$ denotes a generalized inverse of $$A$$.

title: Schur complement


text:
James Croll

James Croll, FRS, (2 January 1821 – 15 December 1890) was a 19th-century Scottish scientist who developed a theory of climate variability based on changes in the Earth's orbit.

Life
James Croll was born in 1821 on the farm of Little Whitefield, near Wolfhill in Perthshire, Scotland, the son of David Croll, mason, and his wife Janet Geddes. He was largely self-educated. At 16 he became an apprentice wheelwright at Collace near Wolfhill, and then because of health problems a tea merchant in Elgin, Moray. In 1848 he married Isabella Macdonald, daughter of John Macdonald and Annabella Sime, of Forres.

In the 1850s he managed a temperance hotel in Blairgowrie, and was then an insurance agent in Glasgow, Edinburgh and Leicester. In 1859, he became a janitor at the museum of the Andersonian University in Glasgow. He was able to use the university library to get access to books, and taught himself physics and astronomy to develop his ideas.

From 1864, Croll corresponded with Sir Charles Lyell, on links between ice ages and variations in the Earth's orbit. He theorized that changes in the Earth's orbit could cause the Gulf Stream to be diverted, bringing less heat to the Arctic. More ice would then lead to more sunlight being reflected, causing a feedback loop. His ideas were published in the Philosophical Magazine in 1864, attributed to "James Croll, Anderson's University".

This led to a position in the Edinburgh office of the Geological Survey of Scotland, as keeper of maps and correspondence, where the director, Sir Archibald Geikie, encouraged his research. He published a number of books and papers which "were at the forefront of contemporary science", including Climate and Time, in Their Geological Relations in 1875. He corresponded with Charles Darwin on erosion by rivers.

In 1876, he was elected Fellow of the Royal Society, and awarded an honorary degree by the University of St Andrews. He retired in 1880 because of ill health.

Death
Croll died on 15 December 1890 at 5 Pitcullen Crescent, Perth, Scotland. He was buried in a family grave in Cargill, Perthshire.

Croll's work has been widely recognised in scientific circles and societies. The highest award of the Quaternary Research Association is the James Croll Medal.

Theory of ice ages
Croll was the leading proponent of an astronomical-based theory of climate change, now known as the "Astronomical Theory of Climate Change". Using formulae for orbital variations developed by Urbain Le Verrier (which had led to the discovery of Neptune), Croll developed a theory of the effects of variations of the Earth's orbit on climate cycles. His idea was that decreases in winter sunlight would favour snow accumulation, and for the first time coupled this to the idea of a positive ice-albedo feedback to amplify the solar variations. Croll further argued that the accumulation of snow would change the pattern of trade winds, leading to the deflection of warming currents like the Gulf Stream, and finally a self-sustaining ice age. He suggested that when orbital eccentricity is high winters will tend to be colder when the Earth is farther from the sun in that season and hence, that during periods of high orbital eccentricity, ice ages occur on 22,000-year cycles in each hemisphere, and alternate between southern and northern hemispheres, lasting approximately 10,000 years each.

Croll's theory predicted multiple ice ages, asynchronous in northern and southern hemispheres, and that the last ice ages should have ended about 80,000 years ago. Evidence was just then emerging of multiple ice ages, and geologists were interested in a theory to explain this. Geologists were not then able to date sediments accurately enough to determine if glaciation was synchronous between the hemispheres, though the limited evidence more pointed towards synchronicity than not. More crucially, estimates of the recession rate of the Niagara Falls indicated that the last ice age ended 6,000 to 35,000 years ago – a large range, but enough to rule out Croll's theory, to those who accepted the measurements.

Croll's work was widely discussed, but by the end of the 19th century, his theory was generally discredited. However, the basic idea of orbitally-forced insolation variations influencing terrestrial temperatures – now known generally as Milankovitch cycles – was further developed by Milutin Milankovitch and eventually, in modified form, triumphed in 1976.

Works

 * 1857: The Philosophy of Theism
 * 1864: XIII. On the Physical Cause of the Change of Climate During Geological Epochs. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 28 (187) 121–137. https://doi.org/10.1080/14786446408643733
 * 1867: XVII. On the Excentricity of the Earth's Orbit and its Physical Relations to the Glacial Epoch. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 33 (221) 119–131. https://doi.org/10.1080/14786446708639757
 * 1875: Climate and Time, in Their Geological Relations, a Theory of Secular Changes of the Earth's Climate. London: Edward Stanford.
 * 1885: Climate and Cosmology
 * 1889: Stellar Evolution and Its Relations to Geological Time
 * 1896: posthumous publication of Autobiographical Sketch of James Croll, With Memoir of His Life and Work, edited by J. C. Irons

title: James Croll


text:
Talk:Definite bilinear form

Definite bilinear forms: symmetric only?
I added the word symmetric, because definite is only defined over symmetric bilinear forms. Eulermatroid (talk) 10:48, 1 February 2012 (UTC)

 * Is this necessarily the case? Any bilinear form can be separated into symmetric and antisymmetric parts: $B(x,y) = B^{+}(x,y) + B^{−}(x,y)$ where $B^{+}(x,y) = (B(x,y) + B(y,x))/2$ and $B^{−}(x,y) = (B(x,y) − B(y,x))/2$.  The associated quadratic form $Q(x) = B(x,x) = B^{+}(x,x)$ depends only on the symmetric part $B^{+}$, but that does not mean that it is only defined when $B = B^{+}$ (i.e. when $B$ is symmetric), and that it would be a matter of definition, not of necessity.  Do you have a reference to substantiate your assertion? — Quondum☏✎ 11:55, 1 February 2012 (UTC)

A square matrices of reell numbers is pos. definite if 1) A = A ^ t and at the same time 2) for every x <> 0; x ^ t * A * x> 0

Prof. Veselic, Fernuniversität Hagen, Methoden der Physik Prof. Luise Unger, Fernuniversität Hagen, Lineare Algebra-2, Eulermatroid (talk) 15:44, 2 February 2012 (UTC)
 * I wouldn't have guessed that definiteness is only defined for symmetric forms, but a brief browse through google books makes it seem the case. I don't have a counterexample of an asymmetric pos def matrix. I think the main goal is to say "a quadratic form is definite" when the outputs have fixed sign, and quadratic forms are associated with symmetric bilinear forms. Rschwieb (talk) 18:14, 2 February 2012 (UTC)
 * Review my logic above. The counterexample of an asymmetric pos-def matrix is trivially easy: take any positive-definite symmetric matrix, and to it add any antisymmetric matrix, and you have it.  Put another way: Any square matrix (symmetric or not) with only positive eigenvalues is positive-definite.  See  for an example of not restricting the definition to symmetric bilinear forms. — Quondum☏✎ 19:49, 2 February 2012 (UTC)

The fact that a given unsymmetric matrice satisfies condition 2) [ x ^ t * A * x> 0]; does not mean that it is pos. definite. Every professor should know that, ask one. 93.199.170.224 (talk) 08:42, 3 February 2012 (UTC)
 * I think the definition should be given for symmetric forms only. For a non-symmetric form to be "definite" in the article's sense, a necessary and sufficient condition is that its symmetric part be definite.  If there are any sources that substantiate this viewpoint, then it can be added later in the article.  But the majority of sources (in my experience) assume symmetry.  Perhaps the reason for this is twofold.  First, many theorems hold for the symmetric case that otherwise do not in the asymmetric.  Second, the asymmetric case isn't actually a useful generalization anyway, for the reason I indicated.   Sławomir Biały  (talk) 11:31, 3 February 2012 (UTC)

 * I think that the term "positive definite" has been introduced primarily for quadratic forms. Therefore it is a pity to have two different articles for Definite bilinear form and Definite quadratic form. I propose to merge these two pages, which should not be difficult, as the latter contains only 4 lines. If the merge is done, this discussion would be almost meaningless.
 * By the way the former is also a stub as it should contain, at least, the two following important results.
 * * Over a vector space of finite dimension, all positive definite quadratic forms are equivalent in the sense that they have the same matrix on well chosen bases. It follows that a Euclidean vector space is simply a vector space equipped with a positive definite quadratic form.
 * * If f is a two times differentiable function of several real variables and x is a value of its variable corresponding to a local minimum of f, then the gradient of f is null at x and the part of order 2 of its Taylor expansion (associated to its Hessian matrix) is a positive semidefinite quadratic form. Conversely, if the gradient is null and the Hessian is positive definite, then x is a local minimum.
 * D.Lazard (talk) 17:18, 3 February 2012 (UTC)

 * I would support a merge into Definite quadratic form, which should show how the associated symmetric bilinear form is determined by the quadratic form. — Quondum☏✎ 17:49, 3 February 2012 (UTC)

title: Talk:Definite bilinear form


text:
User:Renato Caniatti~enwiki/Grafici climatici

 * Template


text:
User:Pibwl

PIBWL is a wikipedian since 2003 (and, I'm afraid, wikipediholic ;-)

de:Benutzer:Pibwl pl:wikipedysta:Pibwl

title: User:Pibwl