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==History==
Matrices have a long history of application in solving [[linear equations]] but they were known as arrays until the 1800s. The [[Chinese mathematics|Chinese text]] ''[[The Nine Chapters on the Mathematical Art]]'' is the first example of the use of array methods to solve [[System of linear equations|simultaneous equations]],<ref>{{Harvard citations |last1=Shen |last2=Crossley |last3=Lun |year=1999 |nb=yes }} cited by {{Harvard citations | last1=Bretscher | year=2005|nb=yes|loc=p. 1}}</ref> including the concept of [[determinant|determinants.]] In 1545 Italian mathematician Girolamo Cardano brought the method to Europe when he published ''Ars Magna''.<ref name=":1">Discrete Mathematics 4th Ed. Dossey, Otto, Spense, Vanden Eynden, Published by Addison Wesley, October 10, 2001 ISBN 978-0321079121 | p.564-565</ref> The [[Japanese mathematics|Japanese mathematician]] [[Seki Kowa|Seki]] used the same array methods to solve simultaneous equations in 1683.<ref>{{cite book |last1=Needham |first1=Joseph |authorlink1=Joseph Needham |last2=Wang Ling |authorlink2=Wang Ling (historian) |title=Science and Civilisation in China |url=http://books.google.com/books?id=jfQ9E0u4pLAC&pg=PA117 |volume=III |year=1959 |publisher=Cambridge University Press |location=Cambridge |isbn=9780521058018 |page=117}}</ref> The Dutch Mathematician'' ''[[Jan de Witt]] represented transformations using arrays in his 1659 book ''Elements of Curves'' (1659).<ref name=":0">Discrete Mathematics 4th Ed. Dossey, Otto, Spense, Vanden Eynden, Published by Addison Wesley, October 10, 2001 ISBN 978-0321079121 | p.564</ref> Between 1700 and 1710
The term "matrix" ([[Latin]] for "womb", derived from ''[[wikt:mater#Latin|mater]]''—mother<ref>{{Citation |url=http://www.merriam-webster.com/dictionary/matrix |title=Merriam–Webster dictionary |accessdate=April 20, 2009 |publisher=[[Merriam–Webster]] }}</ref>) was coined by James Joseph [[James Joseph Sylvester|Sylvester]] in 1850,<ref>Although many sources state that J. J. Sylvester coined the mathematical term "matrix" in 1848, Sylvester published nothing in 1848. (For proof that Sylvester published nothing in 1848, see: J. J. Sylvester with H. F. Baker, ed., ''The Collected Mathematical Papers of James Joseph Sylvester'' (Cambridge, England: Cambridge University Press, 1904), [http://books.google.com/books?id=r-kZAQAAIAAJ&pg=PR6#v=onepage&q&f=false vol. 1.]) His earliest use of the term "matrix" occurs in 1850 in: J. J. Sylvester (1850) "Additions to the articles in the September number of this journal, "On a new class of theorems," and on Pascal's theorem," ''The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science'', '''37''' : 363-370. [http://books.google.com/books?id=CBhDAQAAIAAJ&pg=PA369#v=onepage&q&f=false From page 369]: "For this purpose we must commence, not with a square, but with an oblong arrangement of terms consisting, suppose, of m lines and n columns. This will not in itself represent a determinant, but is, as it were, a Matrix out of which we may form various systems of determinants … "</ref> who understood a matrix as an object giving rise to a number of determinants today called [[minor (linear algebra)|minor]]s, that is to say, determinants of smaller matrices that derive from the original one by removing columns and rows. In an 1851 paper, Sylvester explains:
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