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Talk:Brooklyn Bridge

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Discrepancy in bridge heights
The bridge deck height of 133' above MHW cited in the New York City Landmarks Preservation Commission application of August 24, 1967 is, it appears, the most current readily available dimension for the navigational clearance of that structure. There is (or may be) a more recent measurement, perhaps on a US Government navigational chart based on NAVD 88 (see below), but I am unable to turn one up online.

The LPCA figure of 133' is based on a survey known as the National Geodetic Vertical Datum of 1929 (NGVD 29) (NGVD 29). It superseded any prior measurements, such as that made when the Brooklyn Bridge was completed in 1883 and published as 135' in the 1914 edition of The World Almanac & Book of Facts formerly cited at the BB article.

NGVD 29 (and measurements based on it) have themselves been superseded, replaced by the North American Vertical Datum of 1988 (NAVD 88), a Tidal Datum based on an 18.6 year lunar nodal cycle (and well overdue to be replaced by one based on a subsequent cycle already several years underway, the Datum of 2022 ).

If anyone can find a navigational clearance for the BB based on NAVD 88 it would take precedence over the dimension in the LPCA. Yours, Wikiuser100 (talk) 21:14, 20 December 2019 (UTC)

 * Guys, I have found the most current possible reference and dimension for the vertical clearance of the deck of the Brooklyn Bridge. It is off the current NOAA National Ocean Service Coast Survey navigational chart of the Hudson and East River between 67th street and Governors Island, last corrected October 1, 2019: .  It gives the navigational clearance of the bridge as 127'.  (And even lists a temporary dimension of 110' beneath its movable repair platforms.)  So that is the official dimension from the low point of the bridge deck to Mean High Water (itself established by the North American Vertical Datum of 1988 (NAVD 88), and the basis for all depths, soundings, and elevations on the map).  I will make the appropriate change and citation at the main article.  Yours, Wikiuser100 (talk) 18:04, 21 December 2019 (UTC)
 * Thanks for the find. I think it may have something to do with different, more accurate methods of measurement, as well as sea level changes. In any case, this puts a whole new perspective on the height of the span. epicgenius (talk) 20:40, 21 December 2019 (UTC)
 * . A change of 2' over a century due to more accurate methods/technologies and sea level changes, I could definitely see that - and expected we would (or already had, from 135' to 133').  A figure of 127' - which is unambiguously on the NOAA nav chart updated through this past October - I did not see coming.  And can't explain.  But indeed anticipate a couple of inch change with the arrival of the Datum of 2022, which uses satellite-based GPS and sophisticated gravimetric modeling rather than the "intermediate" technologies (of advanced manual measurement, carried out "boots on the ground", available prior to 1988).  Which includes some (accelerating) sea level rise due to climate change.
 * According to Wikipedia's article on Air draft real time navigational clearance is now being measured in selected areas via laser, and accessible via wireless link to ship captains and harbor pilots. This, as you know, can be mighty important on very large and tall vessels.  The ginormous for its day USS Forrestal (CV-59), arguably the US' 1st supercarrier and largest ship ever at its commissioning in 1955, was designed so its two folding masts could clear the Brooklyn Bridge (and pass under the 135' Manhattan Bridge) en route to the then still important Navy Yard at Wallabout Bay .  It's a bad day for everyone when they don't and things go crunch.
 * Today's supercarriers (cruise ships, and container ships) are much, much higher, well in excess of 200'. I enjoyed watching once an entire fleet arm steam into San Francisco Bay from a vantage near Seal Rocks, with a score of escort ships parading under the Golden Gate Bridge as the tide fell, waiting the synchronized arrival of, if I recall correctly, the massive USS Enterprise (CVN-65) at low tide, which slowed and lollygagged for a spell while its mast was stepped before venturing beneath the 220' Golden Gate.  You could imagine every person on board holding their breath while everyone on shore gaped, as it did not seem possible to us at Lands End it would fit under, so pronounced was the optical illusion of our line of sight.  And never does from onboard.  Admirals lose stars, or stars and anchors, when someone goofs.  Yours, Wikiuser100 (talk) 02:45, 22 December 2019 (UTC)

One of the oldest?
Hi, The lede claims that "it is one of the oldest roadway bridges in the United States." Since the oldest, the Frankford Avenue Bridge was built in 1697 and the Kingston Bridge (Kingston, New Jersey) in 1798 (7th oldest according to this website), I get the feeling that there were plenty more constructed before 1883. What to do? A cn seems a bit harsh. In the third para: "Only vehicular, pedestrian, and bicycle traffic traffic are permitted, with commercial vehicles being banned." I would suggest "Only private vehicular...", and delete one of the "traffic"s, which seems to have escaped the notice of the the GA reviewer. MinorProphet (talk) 09:17, 22 January 2020 (UTC)
 * Thanks for the comments. Yes a cn would be kind of harsh, and a bit wrong (the correct tag would be disputed-inline). I removed that because it obviously is not true, and not cited in the body. I believe resolved your second concern about repeated "traffic". I really should've gotten that to WP:GOCE, since I wrote the lead on the fly. epicgenius (talk) 23:30, 24 January 2020 (UTC)
 * After re-reading the intro, may I say what a pleasure indeed it is to read a lede that others may heed and take as a creed. >MinorProphet (talk) 01:22, 27 January 2020 (UTC)

Comment by 2605:a000:d744:fc00:ec5d:d625:3676:a33f
I believe the Roebling suspension in Cincinnati is an older steel wire suspension bridge. It was completed in 1867 and is the model for the Brooklyn Bridge. Built by John Roebling. Same designer as the Brooklyn Bridge. The first was the Wheeling Suspension Bridge opened in 1849. Reference Wikipedia. Comment moved from the article to talk. Dreamy Jazz 🎷 talk to me | my contributions 00:26, 25 February 2020 (UTC)
 * , thanks for the catch. Have fixed that now. epicgenius (talk) 14:31, 27 February 2020 (UTC)

comment about Joseph Henderson
An editor trimmed a link about Joseph Henderson, stating that it was unreferenced. However, the second reference given says this: Captain Joseph Henderson, a Sandy Hook pilot, was the next   witness called. He testified as to  the difficulties  masters  of ships  would experience  in  bringing   their  ships  under   the   bridge   when completed. Perhaps there was some other reason for trimming the link TEDickey (talk) 19:02, 17 July 2020 (UTC)
 * , It was inserted by a Henderson family member who has been going around looking for excuse to insert Henderson contents into the article for what appears to be more for promoting his family heritage more so than improving the encyclopedia. There is a discussion at COI Noticeboard. Graywalls (talk) 03:11, 19 July 2020 (UTC)

Modern video of Brooklyn Bridge
I have just uploaded a video I took of Brooklyn Bridge in 2019. If anyone thinks it is suitable for the article do please place it wherever may be appropriate. Anne (talk) 16:33, 4 January 2021 (UTC)
 * I've positioned the video on the article now, but it might need adjusting R or L. Anne (talk) 13:28, 5 January 2021 (UTC)

I've added a quotation and "the bends"
Under the Caissons section of Construction under History, I've added a quotation from Frank Harris to better convey the human experience of the working conditions. I've also added "the bends" as the commonly known term for decompression sickness at the time. Relevant citation here: Tyrone Madera (talk) 22:14, 11 March 2021 (UTC)

Architect
Sorry if this is not the correct way to make this proposition. I am missing information about the architect. It was Wilhelm Hildenbrand I think somehow it should be mentioned.
 * This isn't correct. As described in the article the bridge was designed by John Roebling, with further work by Washington Roebling.  Hildenbrand was a draftsman who worked for Washington Roebling. Dan Bloch (talk) 06:58, 9 May 2021 (UTC)

Good
I like this article. — Preceding unsigned comment added by 98.183.25.236 (talk) 09:08, 25 March 2022 (UTC)

Reinstatement of motor vehicles
In two locations in the article, the 1922 ban on motor vehicle traffic over the bridge is described. In both cases, the next section discusses motor vehicle traffic on the bridge over 25 years later. At some point, clearly, the ban was lifted, but I don't see a mention of it. This crucial piece of the narrative - which I know nothing about or would add it myself - should be included. MicroProf (talk) 15:57, 24 May 2023 (UTC)
 * @MicroProf, thanks for bringing this up. The ban was lifted on May 12, 1925. I cannot believe that I forgot to add that before. – Epicgenius (talk) 01:44, 19 October 2023 (UTC)

The Great Blowout
I just finished David McCullough's The Great Bridge. The caisson fire and the "Great Blowout" were two separate events. Both of them did occur in the Brooklyn caisson. Unfortunately, I have already loaned away the book and cannot look up the details of each event to correct the text. I will do so if I can find another source. Mark (talk) 21:36, 29 May 2023 (UTC)

Bridge sale scam
Seems like we should have some mention of John McCarthy, who repeatedly sold the bridge and made the "have I got a bridge to sell you..." phrase famous. Some stuff here. Matt Deres (talk) 13:41, 16 April 2024 (UTC)

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

title: Talk:Brooklyn Bridge


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Recipe

A recipe is a set of instructions that describes how to prepare or make something, especially a dish of prepared food. A sub-recipe or subrecipe is a recipe for an ingredient that will be called for in the instructions for the main recipe.

Early examples
The earliest known written recipes date to 1730 BC and were recorded on cuneiform tablets found in Mesopotamia.

Other early written recipes date from approximately 1600 BC and come from an Akkadian tablet from southern Babylonia. There are also works in ancient Egyptian hieroglyphs depicting the preparation of food.

Many ancient Greek recipes are known. Mithaecus's cookbook was an early one, but most of it has been lost; Athenaeus quotes one short recipe in his Deipnosophistae. Athenaeus mentions many other cookbooks, all of them lost.

Roman recipes are known starting in the 2nd century BCE with Cato the Elder's De Agri Cultura. Many authors of this period described eastern Mediterranean cooking in Greek and in Latin. Some Punic recipes are known in Greek and Latin translation.

The large collection of recipes De re coquinaria, conventionally titled Apicius, appeared in the 4th or 5th century and is the only complete surviving cookbook from the classical world. It lists the courses served in a meal as Gustatio (appetizer), Primae Mensae (main course) and Secundae Mensae (dessert). Each recipe begins with the Latin command "Take...," "Recipe...."

Arabic recipes are documented starting in the 10th century; see al-Warraq and al-Baghdadi.

The earliest recipe in Persian dates from the 14th century. Several recipes have survived from the time of Safavids, including Karnameh (1521) by Mohammad Ali Bavarchi, which includes the cooking instruction of more than 130 different dishes and pastries, and Madat-ol-Hayat (1597) by Nurollah Ashpaz. Recipe books from the Qajar era are numerous, the most notable being Khorak-ha-ye Irani by prince Nader Mirza.

King Richard II of England commissioned a recipe book called Forme of Cury in 1390, and around the same time, another book was published entitled Curye on Inglish, "cury" meaning cooking. Both books give an impression of how food for the noble classes was prepared and served in England at that time. The luxurious taste of the aristocracy in the Early Modern Period brought with it the start of what can be called the modern recipe book. By the 15th century, numerous manuscripts were appearing detailing the recipes of the day. Many of these manuscripts give very good information and record the re-discovery of many herbs and spices including coriander, parsley, basil and rosemary, many of which had been brought back from the Crusades.

Modern recipes and cooking advice
With the advent of the printing press in the 16th and 17th centuries, numerous books were written on managing households and preparing food. In Holland and England competition grew between the noble families as to who could prepare the most lavish banquet. By the 1660s, cookery had progressed to an art form, and good cooks were in demand. Many of them published their own books, detailing their recipes in competition with their rivals. Many of these books have been translated and are available online.

By the 19th century, the Victorian preoccupation for domestic respectability brought about the emergence of cookery writing in its modern form. Although eclipsed in fame and regard by Isabella Beeton, the first modern cookery writer and compiler of recipes for the home was Eliza Acton. Her pioneering cookbook, Modern Cookery for Private Families published in 1845, was aimed at the domestic reader rather than the professional cook or chef. This was immensely influential, establishing the format for modern writing about cookery. It introduced the now-universal practice of listing the ingredients and suggested cooking times with each recipe. It included the first recipe for Brussels sprouts. Contemporary chef Delia Smith called Acton "the best writer of recipes in the English language." Modern Cookery long survived Acton, remaining in print until 1914 and available more recently in facsimile.

Acton's work was an important influence on Isabella Beeton, who published Mrs Beeton's Book of Household Management in 24 monthly parts between 1857 and 1861. This was a guide to running a Victorian household, with advice on fashion, child care, animal husbandry, poisons, the management of servants, science, religion, and industrialism. Of the 1,112 pages, over 900 contained recipes. Most were illustrated with coloured engravings. It is said that many of the recipes were plagiarised from earlier writers such as Acton, but the Beetons never claimed that the book's contents were original. It was intended as a reliable guide for the aspirant middle classes.

The American cook Fannie Farmer (1857–1915) published in 1896 her famous work The Boston Cooking School Cookbook which contained some 1,849 recipes.

Components
Modern culinary recipes normally consist of several components
 * The name of the recipe (Origins/History of the dish).
 * Yield: The number of servings that the dish provides.
 * List all ingredients in the order of its use. Describe it in step by step instructions.
 * Listing ingredients by the quantity (Write out abbreviations. Ounces instead of oz).
 * How much time does it take to prepare the dish, plus cooking time for the dish.
 * Necessary equipment used for the dish.
 * Cooking procedures. Temperature and bake time if necessary.
 * Serving procedures (Served while warm/cold).
 * Review of the dish (Would you recommend this dish to a friend?).
 * Photograph of the dish (Optional).
 * Nutritional Value: Helps for dietary restrictions. Includes number of calories or grams per serving.

Earlier recipes often included much less information, serving more as a reminder of ingredients and proportions for someone who already knew how to prepare the dish.

Recipe writers sometimes also list variations of a traditional dish, to give different tastes of the same recipes.

Sub-recipes
A sub-recipe or subrecipe is a recipe for an ingredient that will be called for in the instructions for the main recipe.

Sub-recipes are often for spice blends, sauces, confits, pickles, preserves, jams, chutneys, or condiments. Sometimes the sub-recipe calls for the ingredient to be held for several hours, overnight, or longer, which home cooks sometimes find frustrating as it means the main recipe cannot be made in a single session or day. Sub-recipes discovered late and calling for an ingredient the cook does not have on hand means a special shopping trip or trying to find a substitute.

Sub-recipes, and the cookbooks that contain them, are often described as not being targeted at casual cooks. Reviewers have mentioned finding alternate uses for leftover sub-recipes.

Cookbooks including subrecipes include Christina Tosi's Momofuku Milk Bar (2011) and Terry Bryant's Vegetable Kingdom (2020).

Internet and television recipes
By the mid-20th century, there were thousands of cookery and recipe books available. The next revolution came with the introduction of the TV cooks. The first TV cook in the world was Philip Harben with a show on the BBC called Cookery which premiered in June 1946. A few months later I Love to Eat presented by James Beard became the first such program in the US. TV cookery programs brought recipes to a new audience. In the early days, recipes were available by post from the BBC; later with the introduction of CEEFAX text on screen, they became available on television.

The first Internet Usenet newsgroup dedicated to cooking was net.cooks created in 1982, later becoming rec.food.cooking. It served as a forum to share recipes text files and cooking techniques.

In the U.S. in 2008, there was a renewed focus on cooking at home due to the late-2000s recession. Home cooking in the U.S. was similarly inspired in the early 2020s during the coronavirus pandemic.

Television networks such as the Food Network and magazines are still a major source of recipe information, with international cooks and chefs such as Jamie Oliver, Gordon Ramsay, Nigella Lawson and Rachael Ray having prime-time shows and backing them up with Internet websites giving the details of all their recipes. These were joined by reality TV shows such as Top Chef or Iron Chef, and many Internet sites offering free recipes, but cookery books remain as popular as ever.

title: Recipe


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Row and column spaces

In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the image or range of the corresponding matrix transformation.

Let $$F$$ be a field. The column space of an $m × n$ matrix with components from $$F$$ is a linear subspace of the m-space $$F^m$$. The dimension of the column space is called the rank of the matrix and is at most $min(m, n)$. A definition for matrices over a ring $$R$$ is also possible.

The row space is defined similarly.

The row space and the column space of a matrix $A$ are sometimes denoted as $C(A^{T})$ and $C(A)$ respectively.

This article considers matrices of real numbers. The row and column spaces are subspaces of the real spaces $$\R^n$$ and $$\R^m$$ respectively.

Overview
Let $A$ be an $m$-by-$n$ matrix. Then
 * 1) $rank(A) = dim(rowsp(A)) = dim(colsp(A))$ = number of pivots in any echelon form of $A$,
 * 2) $rank(A)$ = the maximum number of linearly independent rows or columns of $A$.
 * 1) $rank(A)$ = the maximum number of linearly independent rows or columns of $A$.

If one considers the matrix as a linear transformation from $$\mathbb{R}^n$$ to $$\mathbb{R}^m$$, then the column space of the matrix equals the image of this linear transformation.

The column space of a matrix $A$ is the set of all linear combinations of the columns in $A$. If $A = [a_{1} ⋯ a_{n}]$, then $colsp(A) = span(\{a_{1}, ..., a_{n}\})$.

The concept of row space generalizes to matrices over $\C$, the field of complex numbers, or over any field.

Intuitively, given a matrix $A$, the action of the matrix $A$ on a vector $x$ will return a linear combination of the columns of $A$ weighted by the coordinates of $x$ as coefficients. Another way to look at this is that it will (1) first project $x$ into the row space of $A$, (2) perform an invertible transformation, and (3) place the resulting vector $y$ in the column space of $A$. Thus the result $y = Ax$ must reside in the column space of $J$. See singular value decomposition for more details on this second interpretation.

Example
Given a matrix $J$:

J = \begin{bmatrix} 2 & 4 & 1 & 3 & 2\\   -1 & -2 & 1 & 0 & 5\\    1 & 6 & 2 & 2 & 2\\    3 & 6 & 2 & 5 & 1  \end{bmatrix} $$ the rows are $$\mathbf{r}_1 = \begin{bmatrix} 2 & 4 & 1 & 3 & 2 \end{bmatrix}$$, $$\mathbf{r}_2 = \begin{bmatrix} -1 & -2 & 1 & 0 & 5 \end{bmatrix}$$, $$\mathbf{r}_3 = \begin{bmatrix} 1 & 6 & 2 & 2 & 2 \end{bmatrix}$$, $$\mathbf{r}_4 = \begin{bmatrix} 3 & 6 & 2 & 5 & 1 \end{bmatrix}$$. Consequently, the row space of $J$ is the subspace of $$\R^5$$ spanned by $\{ r_{1}, r_{2}, r_{3}, r_{4} \}$. Since these four row vectors are linearly independent, the row space is 4-dimensional. Moreover, in this case it can be seen that they are all orthogonal to the vector $n = [6, −1, 4, −4, 0]$ ($n$ is an element of the kernel of $K$ ), so it can be deduced that the row space consists of all vectors in $$\R^5$$ that are orthogonal to $n$.

Definition
Let $A$ be a field of scalars. Let $A$ be an $m × n$ matrix, with column vectors $v_{1}, v_{2}, ..., v_{n}$. A linear combination of these vectors is any vector of the form
 * $$c_1 \mathbf{v}_1 + c_2 \mathbf{v}_2 + \cdots + c_n \mathbf{v}_n,$$

where $c_{1}, c_{2}, ..., c_{n}$ are scalars. The set of all possible linear combinations of $v_{1}, ..., v_{n}$ is called the column space of $A$. That is, the column space of $A$ is the span of the vectors $v_{1}, ..., v_{n}$.

Any linear combination of the column vectors of a matrix $A$ can be written as the product of $A$ with a column vector:
 * $$\begin{array} {rcl}

A \begin{bmatrix} c_1 \\ \vdots \\ c_n \end{bmatrix} & = & \begin{bmatrix} a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{m1} & \cdots & a_{mn} \end{bmatrix} \begin{bmatrix} c_1 \\ \vdots \\ c_n \end{bmatrix} = \begin{bmatrix} c_1 a_{11} + \cdots + c_{n} a_{1n} \\ \vdots \\ c_{1} a_{m1} + \cdots + c_{n} a_{mn} \end{bmatrix} = c_1 \begin{bmatrix} a_{11} \\ \vdots \\ a_{m1} \end{bmatrix} + \cdots + c_n \begin{bmatrix} a_{1n} \\ \vdots \\ a_{mn} \end{bmatrix} \\ & = & c_1 \mathbf{v}_1 + \cdots + c_n \mathbf{v}_n \end{array}$$

Therefore, the column space of $A$ consists of all possible products $Ax$, for $x ∈ K^{n}$. This is the same as the image (or range) of the corresponding matrix transformation.

Example
If $$A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 2 & 0 \end{bmatrix}$$, then the column vectors are $v_{1} = [1, 0, 2]^{T}$ and $v_{2} = [0, 1, 0]^{T}$. A linear combination of v1 and v2 is any vector of the form $$c_1 \begin{bmatrix} 1 \\ 0 \\ 2 \end{bmatrix} + c_2 \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} c_1 \\ c_2 \\ 2c_1 \end{bmatrix}$$ The set of all such vectors is the column space of $A$. In this case, the column space is precisely the set of vectors $(x, y, z) ∈ R^{3}$ satisfying the equation $z = 2x$ (using Cartesian coordinates, this set is a plane through the origin in three-dimensional space).

Basis
The columns of $A$ span the column space, but they may not form a basis if the column vectors are not linearly independent. Fortunately, elementary row operations do not affect the dependence relations between the column vectors. This makes it possible to use row reduction to find a basis for the column space.

For example, consider the matrix
 * $$A = \begin{bmatrix} 1 & 3 & 1 & 4 \\ 2 & 7 & 3 & 9 \\ 1 & 5 & 3 & 1 \\ 1 & 2 & 0 & 8 \end{bmatrix}.$$

The columns of this matrix span the column space, but they may not be linearly independent, in which case some subset of them will form a basis. To find this basis, we reduce $A$ to reduced row echelon form:
 * $$\begin{bmatrix} 1 & 3 & 1 & 4 \\ 2 & 7 & 3 & 9 \\ 1 & 5 & 3 & 1 \\ 1 & 2 & 0 & 8 \end{bmatrix}

\sim \begin{bmatrix} 1 & 3 & 1 & 4 \\ 0 & 1 & 1 & 1 \\ 0 & 2 & 2 & -3 \\ 0 & -1 & -1 & 4 \end{bmatrix} \sim \begin{bmatrix} 1 & 0 & -2 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & -5 \\ 0 & 0 & 0 & 5 \end{bmatrix} \sim \begin{bmatrix} 1 & 0 & -2 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{bmatrix}.$$ At this point, it is clear that the first, second, and fourth columns are linearly independent, while the third column is a linear combination of the first two. (Specifically, $v_{3} = −2v_{1} + v_{2}$.) Therefore, the first, second, and fourth columns of the original matrix are a basis for the column space:
 * $$\begin{bmatrix} 1 \\ 2 \\ 1 \\ 1\end{bmatrix},\;\;

\begin{bmatrix} 3 \\ 7 \\ 5 \\ 2\end{bmatrix},\;\; \begin{bmatrix} 4 \\ 9 \\ 1 \\ 8\end{bmatrix}.$$ Note that the independent columns of the reduced row echelon form are precisely the columns with pivots. This makes it possible to determine which columns are linearly independent by reducing only to echelon form.

The above algorithm can be used in general to find the dependence relations between any set of vectors, and to pick out a basis from any spanning set. Also finding a basis for the column space of $A$ is equivalent to finding a basis for the row space of the transpose matrix $A^{T}$.

To find the basis in a practical setting (e.g., for large matrices), the singular-value decomposition is typically used.

Dimension
The dimension of the column space is called the rank of the matrix. The rank is equal to the number of pivots in the reduced row echelon form, and is the maximum number of linearly independent columns that can be chosen from the matrix. For example, the 4 × 4 matrix in the example above has rank three.

Because the column space is the image of the corresponding matrix transformation, the rank of a matrix is the same as the dimension of the image. For example, the transformation $$\R^4 \to \R^4$$ described by the matrix above maps all of $$\R^4$$ to some three-dimensional subspace.

The nullity of a matrix is the dimension of the null space, and is equal to the number of columns in the reduced row echelon form that do not have pivots. The rank and nullity of a matrix $n$ with $A$ columns are related by the equation:
 * $$\operatorname{rank}(A) + \operatorname{nullity}(A) = n.\,$$

This is known as the rank–nullity theorem.

Relation to the left null space
The left null space of $A$ is the set of all vectors $x$ such that $x^{T}A = 0^{T}$. It is the same as the null space of the transpose of $A$. The product of the matrix $A^{T}$ and the vector $x$ can be written in terms of the dot product of vectors:
 * $$A^\mathsf{T}\mathbf{x} = \begin{bmatrix} \mathbf{v}_1 \cdot \mathbf{x} \\ \mathbf{v}_2 \cdot \mathbf{x} \\ \vdots \\ \mathbf{v}_n \cdot \mathbf{x} \end{bmatrix},$$

because row vectors of $A^{T}$ are transposes of column vectors $v_{k}$ of $A$. Thus $A^{T}x = 0$ if and only if $x$ is orthogonal (perpendicular) to each of the column vectors of $A$.

It follows that the left null space (the null space of $A^{T}$) is the orthogonal complement to the column space of $A$.

For a matrix $K$, the column space, row space, null space, and left null space are sometimes referred to as the four fundamental subspaces.

For matrices over a ring
Similarly the column space (sometimes disambiguated as right column space) can be defined for matrices over a ring $m$ as
 * $$\sum\limits_{k=1}^n \mathbf{v}_k c_k$$

for any $c_{1}, ..., c_{n}$, with replacement of the vector $K$-space with "right free module", which changes the order of scalar multiplication of the vector $v_{k}$ to the scalar $c_{k}$ such that it is written in an unusual order vector–scalar.

Definition
Let $A$ be a field of scalars. Let $K$ be an $Ac$ matrix, with row vectors $c$. A linear combination of these vectors is any vector of the form
 * $$c_1 \mathbf{r}_1 + c_2 \mathbf{r}_2 + \cdots + c_m \mathbf{r}_m,$$

where $K^{n}$ are scalars. The set of all possible linear combinations of $m × n$ is called the row space of $A$. That is, the row space of $A$ is the span of the vectors $r_{1}, r_{2}, ..., r_{m}$.

For example, if
 * $$A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 1 & 0 \end{bmatrix},$$

then the row vectors are $c_{1}, c_{2}, ..., c_{m}$ and $r_{1}, ..., r_{m}$. A linear combination of $r_{1}, ..., r_{m}$ and $r_{1} = [1, 0, 2]$ is any vector of the form
 * $$c_1 \begin{bmatrix}1 & 0 & 2\end{bmatrix} + c_2 \begin{bmatrix}0 & 1 & 0\end{bmatrix} = \begin{bmatrix}c_1 & c_2 & 2c_1\end{bmatrix}.$$

The set of all such vectors is the row space of $A$. In this case, the row space is precisely the set of vectors $r_{2} = [0, 1, 0]$ satisfying the equation $r_{1}$ (using Cartesian coordinates, this set is a plane through the origin in three-dimensional space).

For a matrix that represents a homogeneous system of linear equations, the row space consists of all linear equations that follow from those in the system.

The column space of $A$ is equal to the row space of $r_{2}$.

Basis
The row space is not affected by elementary row operations. This makes it possible to use row reduction to find a basis for the row space.

For example, consider the matrix
 * $$A = \begin{bmatrix} 1 & 3 & 2 \\ 2 & 7 & 4 \\ 1 & 5 & 2\end{bmatrix}.$$

The rows of this matrix span the row space, but they may not be linearly independent, in which case the rows will not be a basis. To find a basis, we reduce $A$ to row echelon form:

$(x, y, z) ∈ K^{3}$, $z = 2x$, $A^{T}$ represents the rows.

\begin{align} \begin{bmatrix} 1 & 3 & 2 \\ 2 & 7 & 4 \\ 1 & 5 & 2\end{bmatrix} &\xrightarrow{\mathbf{r}_2-2\mathbf{r}_1 \to \mathbf{r}_2} \begin{bmatrix} 1 & 3 & 2 \\ 0 & 1 & 0 \\ 1 & 5 & 2\end{bmatrix} \xrightarrow{\mathbf{r}_3-\,\,\mathbf{r}_1 \to \mathbf{r}_3} \begin{bmatrix} 1 & 3 & 2 \\ 0 & 1 & 0 \\ 0 & 2 & 0\end{bmatrix} \\ &\xrightarrow{\mathbf{r}_3-2\mathbf{r}_2 \to \mathbf{r}_3} \begin{bmatrix} 1 & 3 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 0\end{bmatrix} \xrightarrow{\mathbf{r}_1-3\mathbf{r}_2 \to \mathbf{r}_1} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 0\end{bmatrix}. \end{align} $$ Once the matrix is in echelon form, the nonzero rows are a basis for the row space. In this case, the basis is $r_{1}$. Another possible basis $r_{2}$ comes from a further reduction.

This algorithm can be used in general to find a basis for the span of a set of vectors. If the matrix is further simplified to reduced row echelon form, then the resulting basis is uniquely determined by the row space.

It is sometimes convenient to find a basis for the row space from among the rows of the original matrix instead (for example, this result is useful in giving an elementary proof that the determinantal rank of a matrix is equal to its rank). Since row operations can affect linear dependence relations of the row vectors, such a basis is instead found indirectly using the fact that the column space of $r_{3}$ is equal to the row space of $A$. Using the example matrix $A$ above, find $\{ [1, 3, 2], [2, 7, 4] \}$ and reduce it to row echelon form:

A^{\mathrm{T}} = \begin{bmatrix} 1 & 2 & 1 \\ 3 & 7 & 5 \\ 2 & 4 & 2\end{bmatrix} \sim \begin{bmatrix} 1 & 2 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 0\end{bmatrix}. $$

The pivots indicate that the first two columns of $\{ [1, 0, 2], [0, 1, 0] \}$ form a basis of the column space of $A^{T}$. Therefore, the first two rows of $A$ (before any row reductions) also form a basis of the row space of $A$.

Dimension
The dimension of the row space is called the rank of the matrix. This is the same as the maximum number of linearly independent rows that can be chosen from the matrix, or equivalently the number of pivots. For example, the 3 × 3 matrix in the example above has rank two.

The rank of a matrix is also equal to the dimension of the column space. The dimension of the null space is called the nullity of the matrix, and is related to the rank by the following equation:
 * $$\operatorname{rank}(A) + \operatorname{nullity}(A) = n,$$

where $A$ is the number of columns of the matrix $n$. The equation above is known as the rank–nullity theorem.

Relation to the null space
The null space of matrix $A$ is the set of all vectors $A^{T}$ for which $A^{T}$. The product of the matrix $A$ and the vector $A^{T}$ can be written in terms of the dot product of vectors:
 * $$A\mathbf{x} = \begin{bmatrix} \mathbf{r}_1 \cdot \mathbf{x} \\ \mathbf{r}_2 \cdot \mathbf{x} \\ \vdots \\ \mathbf{r}_m \cdot \mathbf{x} \end{bmatrix},$$

where $x$ are the row vectors of $A$. Thus $Ax = 0$ if and only if $x$ is orthogonal (perpendicular) to each of the row vectors of $A$.

It follows that the null space of $A$ is the orthogonal complement to the row space. For example, if the row space is a plane through the origin in three dimensions, then the null space will be the perpendicular line through the origin. This provides a proof of the rank–nullity theorem (see dimension above).

The row space and null space are two of the four fundamental subspaces associated with a matrix $A$ (the other two being the column space and left null space).

Relation to coimage
If $A$ and $V$ are vector spaces, then the kernel of a linear transformation $r_{1}, ..., r_{m}$ is the set of vectors $Ax = 0$ for which $x$. The kernel of a linear transformation is analogous to the null space of a matrix.

If $W$ is an inner product space, then the orthogonal complement to the kernel can be thought of as a generalization of the row space. This is sometimes called the coimage of $V$. The transformation $T$ is one-to-one on its coimage, and the coimage maps isomorphically onto the image of $T$.

When $T$ is not an inner product space, the coimage of $V$ can be defined as the quotient space $T: V → W$.

title: Row and column spaces


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Australian Open

The Australian Open is a tennis tournament held annually at Melbourne Park in Melbourne, Victoria, Australia. The tournament is the first of the four Grand Slam tennis events held each year, preceding the French Open, Wimbledon and the US Open. The Australian Open starts in the middle of January and continues for two weeks coinciding with the Australia Day holiday. It features men's and women's singles; men's, women's and mixed doubles; junior's championships; and wheelchair, legends and exhibition events. Until 1987, it was played on grass courts, but since then three types of hardcourt surfaces have been used: green-coloured Rebound Ace up to 2007 and blue Plexicushion from 2008 to 2019. Since 2020, it has been played on blue GreenSet.

First held in 1905 as the Australasian championships, the Australian Open has grown to become one of the biggest sporting events in the Southern Hemisphere. Nicknamed "the happy slam", the Australian Open is the highest attended Grand Slam event, with more than 1,100,000 people attending the 2024 tournament, including qualifying. It was also the first Grand Slam tournament to feature indoor play during wet weather or extreme heat with its three primary courts, Rod Laver Arena, John Cain Arena and the refurbished Margaret Court Arena equipped with retractable roofs.

The Australian Open is known for its fast-paced and aggressive style of play. The tournament has been held at the Melbourne Park complex since 1988, and is a major contributor to the Victorian economy; the 2020 Australian Open injected $387.7 million into the state's economy, while over the preceding decade the Australian Open had contributed more than $2.71 billion in economic benefits to Victoria and generated 1775 jobs for the state, with these jobs being predominantly in the accommodation, hotels, cafés and trade services sectors.

History
 The Australian Open is managed by Tennis Australia, formerly the Lawn Tennis Association of Australia (LTAA), and was first played at the Warehouseman's Cricket Ground in Melbourne in November 1905. The facility is now known as the Albert Reserve Tennis Centre, and was a grass court.

The tournament was first known as the Australasian Championships. It became the Australian Championships in 1927. Then, in 1969, it became the Australian Open. Since 1905, it has been staged 110 times in five Australian cities: Melbourne (66 times), Sydney (17 times), Adelaide (15 times), Brisbane (7 times), Perth (3 times), and two New Zealand cities: Christchurch (1906) and Hastings (1912).

Although it began in 1905, the International Lawn Tennis Federation (ILTF) did not designated it a major championship until 1924, following a meeting held in 1923. The tournament committee changed the structure of the tournament to include seeding at that time. In the period of 1916–1918, no tournament was organized due to World War I.

During World War II, the tournament was not held from 1941 to 1945. In 1972, it was decided to stage the tournament in Melbourne each year because it attracted the biggest patronage of any Australian city. The tournament was played at the Kooyong Lawn Tennis Club from 1972 until its move to the new Flinders Park complex in 1988.

The new facilities at Flinders Park were envisaged to meet the demands of a tournament that had outgrown Kooyong's capacity. The move to Flinders Park was an immediate success, with a 90 percent increase in attendance in 1988 (266,436) on the previous year at Kooyong (140,000).

Because of Australia's geographic remoteness, very few foreign players entered this tournament in the early 20th century. In the 1920s, the trip by ship from Europe to Australia took about 45 days. The first tennis players who came by boat were the US Davis Cup players in November 1946. Even inside Australia, many players could not travel easily. When the tournament was held in Perth, no one from Victoria or New South Wales crossed by train, a distance of about 3000 km between the East and West coasts. In Christchurch in 1906, of a small field of 10 players, only two Australians attended and the tournament was won by a New Zealander. The first tournaments of the Australasian Championships suffered from the competition of the other Australasian tournaments. Before 1905, all Australian states, and New Zealand, had their own championships; the first being organised in 1880 in Melbourne and called the Championship of the Colony of Victoria (later the Championship of Victoria). In those years, the best two players – Australian Norman Brookes (whose name is now written on the men's singles cup) and New Zealander Anthony Wilding – almost did not play this tournament.

Brookes took part once and won in 1911, and Wilding entered and won the competition twice (1906 and 1909). Their meetings in the Victorian Championships (or at Wimbledon) helped to determine the best Australasian players. Even when the Australasian Championships were held in Hastings, New Zealand, in 1912, Wilding, though three times Wimbledon champion, did not come back to his home country. It was a recurring problem for all players of the era. Brookes went to Europe only three times, where he reached the Wimbledon Challenge Round once and then won Wimbledon twice.

Thus, many players had never played the Austral(as)ian amateur or open championships: the Doherty brothers, William Larned, Maurice McLoughlin, Beals Wright, Bill Johnston, Bill Tilden, René Lacoste, Henri Cochet, Bobby Riggs, Jack Kramer, Ted Schroeder, Pancho Gonzales, Budge Patty, and others, while Brookes, Ellsworth Vines, Jaroslav Drobný, came just once. Even in the 1960s and 1970s, when travel was less difficult, leading players such as Manuel Santana, Jan Kodeš, Manuel Orantes, Ilie Năstase (who only came once, when 35 years old) and Björn Borg came rarely or not at all.

Open era
Beginning in 1969, when the first Australian Open was held on the Milton Courts at Brisbane, the tournament was open to all players, including professionals who were not allowed to play the traditional circuit. Nevertheless, except for the 1969 and 1971 tournaments, many of the best players missed this championship until 1982, because of the remoteness, the inconvenient dates (around Christmas and New Year's Day) and the low prize money. In 1970, George MacCall's National Tennis League, which employed Rod Laver, Ken Rosewall, Andrés Gimeno, Pancho Gonzales, Roy Emerson and Fred Stolle, prevented its players from entering the tournament because the guarantees were insufficient. The tournament was won by Arthur Ashe. In 1983, Ivan Lendl, John McEnroe and Mats Wilander entered the tournament. Wilander won the singles title and both his Davis Cup singles rubbers in the Swedish loss to Australia at Kooyong shortly after. Following the 1983 Australian Open, the International Tennis Federation prompted the Lawn Tennis Association of Australia to change the site of the tournament, because the Kooyong stadium was then inappropriate to serve such a big event. In 1988 the tournament was first held at Flinders Park (later renamed Melbourne Park). The change of the venue also led to a change of the court surface from grass to a hard court surface known as Rebound Ace.

Mats Wilander was the only player to win the tournament on both grass and hard courts. In 2008, after being used for 20 years, the Rebound Ace was replaced by a cushioned, medium-paced, acrylic surface known as Plexicushion Prestige. Roger Federer and Serena Williams are the only players to win the Australian Open on both Rebound Ace and Plexicushion Prestige. The main benefits of the new surface are better consistency and less retention of heat because of a thinner top layer. This change was accompanied by changes in the surfaces of all lead-up tournaments to the Australian Open. The change was controversial because of the new surface's similarity to DecoTurf, the surface used by the US Open.

Before the Melbourne Park stadium era, tournament dates fluctuated as well, in particular in the early years because of the climate of each site or exceptional events. For example, the 1919 tournament was held in January 1920 (the 1920 tournament was played in March) and the 1923 tournament in Brisbane took place in August when the weather was not too hot and wet. After a first 1977 tournament was held in December 1976 – January 1977, the organisers chose to move the next tournament forward a few days, then a second 1977 tournament was played (ended on 31 December), but this failed to attract the best players. From 1982 to 1985, the tournament was played in mid-December. Then it was decided to move the next tournament to mid-January (January 1987), which meant no tournament was organized in 1986. Since 1987, the Australian Open date has not changed (except for 2021, when it was postponed by three weeks to February due to the COVID-19 pandemic). Some top players, including Roger Federer and Rafael Nadal, have said in the past that the tournament is held too soon after the Christmas and New Year holidays, and expressed a desire to consider shifting the tournament to February. Such a change, however, would move the tournament outside Australia's summer school holiday period, potentially impacting attendance figures.

Prior to 1996, the Australian Open rewarded fewer ATP rankings points than the other three Grand Slam tournaments. The reason cited by the ATP was the prize money offered by the Australian Open was far less than the other three majors.

Melbourne Park expansion
New South Wales and overseas authorities proposed becoming the new hosts of the tournament in 2008, though such a move never materialised. In any case, it was around this time the Melbourne Park precinct commenced upgrades which enhanced facilities for players and spectators.

Notably a retractable roof was placed over Margaret Court Arena, making the Open the first of the four Grand Slams to have retractable roofs available on three of their main courts. The player and administrative facilities, as well as access points for spectators, were improved and the tournament site expanded its footprint out of Melbourne Park into nearby Birrarung Marr. A fourth major show court, seating 5,000 people was completed in late 2021, along with the rest of decade-long redevelopment, which included the Centrepiece ballroom, function and media building, as well as other upgraded facilities for players, administrators and spectators.

In December 2018, tournament organisers announced the Australian Open would follow the examples set by Wimbledon and the US Open and introduce tie-breaks in the final sets of men's and women's singles matches. Unlike Wimbledon and the US Open, which initiated conventional tie-breaks at 12–12 games and 6–6 games respectively, the Australian Open utilises a first to 10 points breaker at 6 games all. In 2020, the tournament organisers decided to replace the official court manufacturer to GreenSet, though retained the iconic blue cushioned acrylic hardcourt.

In 2021, in an effort to reduce the number of staff on-site due to the COVID-19 pandemic, all matches used electronic line judging. It marked the first-ever Grand Slam tournament to exclusively use electronic line judging; the 2020 US Open used it for matches outside of the two main stadium courts. The Australian Open produced a range of NFTs in 2022.

Starting in 2024, the Australian Open began on a Sunday, one day earlier than usual. Day sessions on Rod Laver Arena and Margaret Court Arena featured a minimum of two matches (down from three) in an effort to reduce the possibility of matches finishing in the early hours of the following morning.

Courts
The Australian Open is played at Melbourne Park, which is located in the Melbourne Sports and Entertainment Precinct; the event moved to this site in 1988. Currently three of the courts have retractable roofs, allowing play to continue during rain and extreme heat. As of 2017, spectators can also observe play at Show Courts 2 and 3, which have capacities of 3,000 each, as well as at Courts 4–15, 19 and 20 with the aid of temporary seating grandstands of capacity anywhere from 50 to 2,500.

Construction of a new 5,000 seat capacity stadium began in 2019 as part of a $271 million redevelopment of the precinct. The new stadium, Kia Arena, was unveiled by Australian Open officials on 22 November 2021.

From 2008 to 2019, all of the courts used during the Australian Open were hard courts with Plexicushion acrylic surfaces (though Melbourne Park does have eight practice clay courts which are not used for the tournament). This replaced the Rebound Ace surface used from the opening of Melbourne Park. The ITF rated the surface's speed as medium. Since 2020, the courts have used a GreenSet surface.

Ranking points
Ranking points for the men (ATP) and women (WTA) have varied at the Australian Open through the years but presently players receive the following points:

Prize money and trophies
The prize money awarded in the men's and women's singles tournaments is distributed equally. The total prize money for the 2024 tournament in Australian dollars is AUD $86,500,000. The prize money distribution is as follows:
 * Doubles prize money is per team.

Trophies
The names of the tournament winners are inscribed on the perpetual trophy cups. In 2013 ABC Bullion, a Pallion company, was awarded the rights to make the Cups. The cups are produced by W.J. Sanders a sister division within Pallion and takes over 250 hours to produce.

 * The women's singles winner is presented with the Daphne Akhurst Memorial Cup.
 * The men's singles winner is presented with the Norman Brookes Challenge Cup.

Former champions

 * Men's singles, winners of the Norman Brookes Challenge Cup.
 * Women's singles, winners of the Daphne Akhurst Memorial Cup.
 * Men's doubles
 * Women's doubles
 * Mixed doubles
 * All champions

Records

 * Unlike the other three Grand Slam tournaments, which became open in 1968, the Australian tournament opened to professionals in 1969.

Media coverage and attendance
From 1973 to 2018, the Seven Network served as the host broadcaster of the Australian Open. In March 2018, it was announced that the Nine Network had acquired the rights to the tournament beginning in 2020, for a period of five years. The network later bought the rights for the 2019 tournament as well. The Open's broadcast rights are lucrative in the country, as it occurs near the end of the Summer non-ratings season — which gives its broadcaster opportunities to promote their upcoming programming lineup. As of 2022, Nine has extended its rights to the Australian Open until 2029.

In Europe the tournament is broadcast on Eurosport. Other broadcasters in the region have included the BBC in the United Kingdom, SRG in Switzerland, NOS in Netherlands and RTS in Serbia. In the United Kingdom, the BBC dropped its live coverage of the 2016 tournament just a month before the start due to budget cuts, leaving Eurosport as the exclusive live broadcaster.

Elsewhere, beIN Sports broadcasts it into the Middle East and northern Africa, and SuperSport in sub-Sahara Africa. In the United States, the tournament is broadcast on ESPN2, ESPN3 and the Tennis Channel, with limited highlights airing on ABC. The championship matches are televised live on ESPN. While it is broadcast on ESPN International in Central and Latin America. It is broadcast on TSN in Canada.

In the Asia–Pacific region, the tournament is broadcast on five television networks in China, including national broadcaster CCTV, provincial networks Beijing TV, Shanghai Dragon TV and Guangdong TV and English language Star Sports, as well as online on iQIYI Sports. Elsewhere in the region, it is broadcast in Japan by national broadcaster NHK, and pay-TV network Wowow. In the Indian subcontinent, Sony Six has broadcast since 2015 and, in the rest of Asia, it is broadcast on Fox Sports Asia until the network's shutdown in 2021 and the rights is acquired by beIN Sports from 2022 except for Vietnam which will be broadcast on K+.

Attendance
The Australian Open is the most attended Grand Slam. The tournament in 2024 set a new attendance record of 1,110,657 while the single-day attendance record is 94,854, recorded on the 21 January 2023.

The following record of attendance begins in 1987, when the tournament moved from being held in December to in January (the immediate preceding tournament was December 1985). 1987 was the last year that the Kooyong Tennis Club hosted the tournament; since 1988 it has been held at Melbourne Park. The average growth rate over the period covered below is more than 7%. Note that these figures include attendances for the week of qualifying and pre-main tournament events.

 * 2024: 1,110,657
 * 2023: 902,312
 * 2022: 346,468
 * 2021: 130,374
 * 2020: 812,174
 * 2019: 796,435
 * 2018: 743,667
 * 2017: 728,763
 * 2016: 720,363
 * 2015: 703,899
 * 2014: 643,280
 * 2013: 684,457
 * 2012: 686,006
 * 2011: 651,127
 * 2010: 653,860
 * 2009: 603,160
 * 2008: 605,735
 * 2007: 554,858
 * 2006: 550,550
 * 2005: 543,873
 * 2004: 521,691
 * 2003: 512,225
 * 2002: 518,248
 * 2001: 543,834
 * 2000: 501,251
 * 1999: 473,296
 * 1998: 434,807
 * 1997: 391,504
 * 1996: 389,598
 * 1995: 311,678
 * 1994: 332,926
 * 1993: 322,074
 * 1992: 329,034
 * 1991: 305,048
 * 1990: 312,000
 * 1989: 289,023
 * 1988: 244,859
 * 1987: 140,089

title: Australian Open


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title: Talk:Comanche County, Oklahoma


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Talk:Cotton County, Oklahoma

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This article meets the requirements for Class C. Bruin2 (talk) 15:30, 28 September 2013 (UTC)

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title: Talk:Cotton County, Oklahoma


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Talk:Cimarron County, Oklahoma

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No Stoplights
According to the brochure I picked up in Boise City, Cimarron County is the only county in Oklahoma without a single stop light.-WK-70.240.49.16 (talk) 03:11, 17 December 2009 (UTC)

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This article meets the requirements for class C. I havemade the change for WP:Oklahoma Bruin2 (talk) 14:49, 21 August 2013 (UTC)
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title: Talk:Cimarron County, Oklahoma


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Talk:Choctaw County, Oklahoma

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This article meets the requirements for Class C. Bruin2 (talk) 15:20, 28 September 2013 (UTC)

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title: Talk:Choctaw County, Oklahoma


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Talk:List of counties in Oklahoma

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Work on article
I am currently working on this article trying to raise the quality of it. I'm using List of counties in Kentucky as a guide which is currently a Featured List candidate. I've got the easy part done, now to try and find where the names come from. Any help would be appreciated.↔NMajdan •talk 21:01, 27 February 2007 (UTC) _____________________________________________________________ July 12, 2016

The list shows McClain County's origin as "Choctaw land." Here is an excerpt from the article on Purcell, Oklahoma, the county seat of McClain Co.: “Located on the Canadian River, it was called the ‘Queen City of the Chickasaw Nation.’ In 1895, one of the five district courts of the Chickasaw Nation was located in Purcell. . .” One of these articles is wrong.

My grandmother was born in Purcell in 1888. Although she was enrolled as a Choctaw on the Dawes Rolls, we have always understood that she was born in the Chickasaw Nation. I think the origin of McClain Co. in the article is incorrect.

Old-time newspaper editors have always believed in the maxim that if you don’t get the little things right readers won’t believe you on the big things.

Mzee Fulani (talk) 10:51, 12 July 2016 (UTC)Mzee Fulani

Government
Somewhere in wikipedia an article or section should cover the strange? county government in Okla. Each count is divide into 3 districts, each run independently by an elected Commissioner.Jimwelch (talk) 18:14, 21 November 2008 (UTC)

Wikiproject help
Some helpful information on U.S. county lists can be found at WP:COUNTYLISTS. Tom pw (talk) (review) 16:29, 24 June 2007 (UTC)

Table issues?
I'm only somewhat familiar with the mechanics of tables, but it appears that something in the code is throwing off the sorting - several tiny counties appear above Oklahoma County when I attempt to sort by population. Anyone know the solution? Duncan1800 (talk) 21:17, 15 February 2009 (UTC)

Map Issues
I cannot get into the map, but the links on the map for "AL", "BL", and "MA" all incorrectly link to Woods County. Please correct them to link to Alfalfa, Blaine, and Major Counties respectively.

Also, both Tillman and Tulsa Counties are abbreviated "TL." Tulsa should probably be changed to "TU." Tillman could be TL or TI.

Two letter codes
Oklahoma is now putting two letter county codes on license plates. If we can find a source for them, we should probably use those. (McClain County's is ML, not MC, for example.) —Scott5114↗ [EXACT CHANGE ONLY] 04:09, 15 January 2012 (UTC)

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title: Talk:List of counties in Oklahoma


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Talk:Craig County, Oklahoma

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This article meets the requirements for Class C. Bruin2 (talk) 16:13, 25 September 2013 (UTC)

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title: Talk:Craig County, Oklahoma


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Talk:Creek County, Oklahoma

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Sufficient information has been added to move this to "C" class. Bruin2 (talk) 15:33, 27 April 2012 (UTC)
 * Upgraded to C class for WikiProject U.S. Counties. Bruin2 (talk) 00:53, 26 September 2013 (UTC)

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Sand Springs limits
According to openstreetmap (which is trusted by Wikipedia) it has that Sand Springs is barely within the limits of Creek county. On google Maps ( i know not the best but just seeing what that has to offer) it has it within the borders of creek county (although it doesnt immediately show the county). But whilst Oklahoma Historical society only says Tulsa county. And the Oklahoma Postal Code Base says it’s within the borders of all 3 counties.I’ll wait till more opinion on this matter comes, but till then I’ll let I be. But If anyone want to put their opinion in this and help sort this out or contest the decision. references: https://www.openstreetmap.org/relation/184998#map=15/36.0745/-96.2046 https://ok.postcodebase.com/city/SAND%20SPRINGS Jerry Steinfield (talk) 05:34, 16 April 2020 (UTC)

title: Talk:Creek County, Oklahoma


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Talk:Custer County, Oklahoma

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This article meets the requirements for Class C. Bruin2 (talk) 15:37, 28 September 2013 (UTC)

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title: Talk:Custer County, Oklahoma


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Talk:Delaware County, Oklahoma

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The total population in this county in the 2000 census, was it 37077 or 31077? —Preceding unsigned comment added by Zdtrlik (talk • contribs) 16:30, 19 November 2010 (UTC)

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This article meets the requirements for Class C. Bruin2 (talk) 06:18, 16 September 2013 (UTC)
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title: Talk:Delaware County, Oklahoma


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Talk:Dewey County, Oklahoma

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This article meets the requiremnts for Class C. Bruin2 (talk) 15:42, 28 September 2013 (UTC)

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Talk:Ellis County, Oklahoma

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This article meets the requirements for Class C. Bruin2 (talk) 21:19, 9 February 2014 (UTC)

External links modified
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I have just modified 4 one external links on Ellis County, Oklahoma. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20110531210815/http://www.naco.org/Counties/Pages/FindACounty.aspx to http://www.naco.org/Counties/Pages/FindACounty.aspx
 * Added archive http://www.webcitation.org/6YSasqtfX?url=http%3A%2F%2Fwww.census.gov%2Fprod%2Fwww%2Fdecennial.html to http://www.census.gov/prod/www/decennial.html
 * Added archive https://web.archive.org/web/20130911234518/http://factfinder2.census.gov to http://factfinder2.census.gov
 * Added archive https://web.archive.org/web/20160329202250/https://www.ok.gov/elections/documents/20160115%20-%20Registration%20By%20County%20%28vr2420%29.pdf to https://www.ok.gov/elections/documents/20160115%20-%20Registration%20By%20County%20%28vr2420%29.pdf

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External links modified
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 * Added archive https://www.webcitation.org/603g9LETG?url=http://quickfacts.census.gov/qfd/states/40/40045.html to http://quickfacts.census.gov/qfd/states/40/40045.html
 * Corrected formatting/usage for http://www.census.gov/prod/www/decennial.html
 * Corrected formatting/usage for http://factfinder2.census.gov/

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title: Talk:Ellis County, Oklahoma


text:
Talk:Garfield County, Oklahoma

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Article classification
This article meets the requirements for Class C. Bruin2 (talk) 15:45, 28 September 2013 (UTC)

External links modified
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I have just modified 4 external links on Garfield County, Oklahoma. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20110531210815/http://www.naco.org/Counties/Pages/FindACounty.aspx to http://www.naco.org/Counties/Pages/FindACounty.aspx
 * Added tag to http://www.census.gov/popest/data/counties/totals/2015/CO-EST2015-alldata.html
 * Added archive http://www.webcitation.org/6YSasqtfX?url=http%3A%2F%2Fwww.census.gov%2Fprod%2Fwww%2Fdecennial.html to http://www.census.gov/prod/www/decennial.html
 * Added archive https://web.archive.org/web/20130911234518/http://factfinder2.census.gov to http://factfinder2.census.gov
 * Added archive https://web.archive.org/web/20160329202250/https://www.ok.gov/elections/documents/20160115%20-%20Registration%20By%20County%20%28vr2420%29.pdf to https://www.ok.gov/elections/documents/20160115%20-%20Registration%20By%20County%20%28vr2420%29.pdf

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External links modified
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I have just modified 4 external links on Garfield County, Oklahoma. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://www.webcitation.org/604TQGlsL?url=http://quickfacts.census.gov/qfd/states/40/40047.html to http://quickfacts.census.gov/qfd/states/40/40047.html
 * Added archive https://web.archive.org/web/20161110102915/https://www.whitehouse.gov/sites/default/files/omb/bulletins/2015/15-01.pdf to https://www.whitehouse.gov/sites/default/files/omb/bulletins/2015/15-01.pdf
 * Corrected formatting/usage for http://www.census.gov/prod/www/decennial.html
 * Corrected formatting/usage for http://factfinder2.census.gov/

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title: Talk:Garfield County, Oklahoma


text:
Talk:Garvin County, Oklahoma

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Article reclassification
This article meets the requirements for Class C. Bruin2 (talk) 04:45, 14 February 2014 (UTC)

External links modified
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I have just modified 4 external links on Garvin County, Oklahoma. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20110531210815/http://www.naco.org/Counties/Pages/FindACounty.aspx to http://www.naco.org/Counties/Pages/FindACounty.aspx
 * Added tag to http://www.census.gov/popest/data/counties/totals/2015/CO-EST2015-alldata.html
 * Added archive http://www.webcitation.org/6YSasqtfX?url=http%3A%2F%2Fwww.census.gov%2Fprod%2Fwww%2Fdecennial.html to http://www.census.gov/prod/www/decennial.html
 * Added archive https://web.archive.org/web/20130911234518/http://factfinder2.census.gov to http://factfinder2.census.gov
 * Added archive https://web.archive.org/web/20160329202250/https://www.ok.gov/elections/documents/20160115%20-%20Registration%20By%20County%20%28vr2420%29.pdf to https://www.ok.gov/elections/documents/20160115%20-%20Registration%20By%20County%20%28vr2420%29.pdf

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External links modified
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I have just modified 3 external links on Garvin County, Oklahoma. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://www.webcitation.org/604TyKysL?url=http://quickfacts.census.gov/qfd/states/40/40049.html to http://quickfacts.census.gov/qfd/states/40/40049.html
 * Corrected formatting/usage for http://www.census.gov/prod/www/decennial.html
 * Corrected formatting/usage for http://factfinder2.census.gov/

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title: Talk:Garvin County, Oklahoma


text:
Talk:Grady County, Oklahoma

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Article classification
This article meets the requirements for Class C. Bruin2 (talk) 16:15, 16 September 2013 (UTC)
 * Rerated for WikiProject U.S. Counties. Bruin2 (talk) 15:47, 28 September 2013 (UTC)

External links modified
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I have just modified 3 external links on Grady County, Oklahoma. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20110531210815/http://www.naco.org/Counties/Pages/FindACounty.aspx to http://www.naco.org/Counties/Pages/FindACounty.aspx
 * Added tag to http://www.census.gov/popest/data/counties/totals/2015/CO-EST2015-alldata.html
 * Added archive http://www.webcitation.org/6YSasqtfX?url=http%3A%2F%2Fwww.census.gov%2Fprod%2Fwww%2Fdecennial.html to http://www.census.gov/prod/www/decennial.html
 * Added archive https://web.archive.org/web/20130911234518/http://factfinder2.census.gov/ to http://factfinder2.census.gov/

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External links modified
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I have just modified 2 external links on Grady County, Oklahoma. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://www.webcitation.org/604k58r4u?url=http://quickfacts.census.gov/qfd/states/40/40051.html to http://quickfacts.census.gov/qfd/states/40/40051.html
 * Corrected formatting/usage for http://www.census.gov/prod/www/decennial.html

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title: Talk:Grady County, Oklahoma