矩阵的历史成书于西汉末、东汉初的《九章算术》用分离系数法表示线性方程组，自然地得到了其增广矩阵在消元过程中，使用的把某行乘以某一非零实数、从某行中减去另一行等运算技巧，相当于矩阵的初等变换但当时并没有现在理解的矩阵概念，虽然它与现在的矩阵形式上相同，但在当时只是作为线性方程组的标准表示与处理方式矩阵的现代概念在19世纪逐渐形成1801年，德国数学家高斯（F. Gauss，1777-1855)把一个线性变换的全部系数作为一个整体1844年，德国数学家艾森斯坦(F.Eisenstein,1823-1852)讨论了“变换”（矩阵）及其乘积1850年，英国数学家西尔维斯特（James Joseph Sylvester,1814-1897)首先使用了矩阵一词西尔维斯特是犹太人，当他在取得剑桥大学数学荣誉会考1等第2名的优异成绩时，仍被禁止在剑桥大学任教从1841年时他接受过一些较低的职位，做过书记官和律师经过若干年的努力，他终于成为霍普金斯（Hopkins)大学的教授，并于1884年重返英格兰，成为牛津大学教授他开创了美国的纯数学研究，创办了《美国数学杂志》他的主要贡献是组合的思想和从较具体的发展中进行抽象。
1858年，英国数学家凯莱(A.Gayley,1821-1895)发表了《关于矩阵理论的研究报告》他首先将矩阵作为一个独立的数学对象加以研究，并在这个主题上首先发表了一系列文章，因而被认为是矩阵论的创立者他给出了现在通用的一系列定义，如两个矩阵的相等、零矩阵、单位矩阵、两个矩阵的和、一个数与一个矩阵的数量积、两个矩阵的积、矩阵的逆、转置矩阵等凯莱注意到矩阵乘法是可结合的，但一般不可交换，而且m×n矩阵只能用n×p矩阵去右乘1854年，法国数学家埃尔米特(C.Hermite,1822-1901) 使用了“正交矩阵”这一术语，但它的正式定义直到1878年才由德国数学家费罗贝尼乌斯(F.G.Frobenius，1849-1917)发表1879年，费罗贝尼乌斯引入了矩阵的秩的概念至此，矩阵的体系基本上建立起来了The History of Matriceshttp://www.ualr.edu/lasmoller/matrices.htmlThe history of matrices goes back to ancient times! But the term "matrix" was not applied to the concept until 1850. "Matrix" is the Latin word for womb, and it retains that sense in English. It can also mean more generally any place in which something is formed or produced.The origins of mathematical matrices lie with the study of systems of simultaneous linear equations. An important Chinese text from between 300 BC and AD 200, Nine Chapters of the Mathematical Art (Chiu Chang Suan Shu), gives the first known example of the use of matrix methods to solve simultaneous equations.In the treatise's seventh chapter, "Too much and not enough," the concept of a determinant first appears, nearly two millennia before its supposed invention by the Japanese mathematician Seki Kowa in 1683 or his German contemporary Gottfried Leibnitz (who is also credited with the invention of differential calculus, separately from but simultaneously with Isaac Newton).More uses of matrix-like arrangements of numbers appear in chapter eight, "Methods of rectangular arrays," in which a method is given for solving simultaneous equations using a counting board that is mathematically identical to the modern matrix method of solution outlined by Carl Friedrich Gauss (1777-1855), also known as Gaussian elimination.The term "matrix" for such arrangements was introduced in 1850 by James Joseph Sylvester. Sylvester, incidentally, had a (very) brief career at the University of Virginia, which came to an abrupt end after an enraged Sylvester hit a newspaper-reading student with a sword stick and fled the country, believing he had killed the student! Since their first appearance in ancient China, matrices have remained important mathematical tools. Today, they are used not simply for solving systems of simultaneous linear equations, but also for describing the quantum mechanics of atomic structure, designing computer game graphics, analyzing relationships, and even plotting complicated dance steps! The elevation of the matrix from mere tool to important mathematical theory owes a lot to the work of female mathematician Olga Taussky Todd (1906-1995), who began by using matrices to analyze vibrations on airplanes during World War II and became the torchbearer for matrix theory.For more information:http://www-history.mcs.st-andrews.ac.uk/HistTopics/Matrices_and_determinants.htmlWords and expressionswomb |wu:m|: (in woman and other female mammals) organ in which offspring is carried and nourished while it develops before birth.millennium |mi’leniəm| (pl millennia): period of 1000 years.treatise |’tri:tiz| ~ (on sth): long written work dealing systematically with one subject. torchbearer References[1] http://www.ualr.edu/lasmoller/matrices.html[2] 李春华．中国古代数学的辉煌成就[J]．通化师范学院学报, 2003, 24(2):103-106．[3] 刘洪元．高斯消元法是中国古法[J]．沈阳农业大学学报, 2003, 34(1): 56-58．[4] 纪志刚．华蘅芳《积较术》的矩阵算法思想[J]．内蒙古师范大学学报: 自然科学版1990, (2): 46-51．[5] 张素亮．《九章算术》中关于矩阵的研究．枣庄师专学报 1990,7(4):72-75．3矩阵介绍。