In mathematics, a matrix (the Matrix) is a rectangular array arranged in accordance with a complex or real number set, from the first matrix coefficients and constants of the equation constituted. The concept of the 19th century by the British mathematician Kelly was first proposed.
Matrix is a common tool in higher algebra, also common in applied mathematics and statistical analysis in. In physics, in the matrix circuit, mechanics, optics and quantum physics have applications; computer science, three-dimensional animation will be needed by the matrix. Matrix operations is an important issue in the field of numerical analysis. The simple matrix matrix into the matrix compositions can simplify the calculation in theory and practical applications. Some widely used and a special form of a matrix, such as sparse matrix and quasi-diagonal matrix, there is a specific algorithm for fast operation. In the field of astrophysics, quantum mechanics, there will be an infinite-dimensional matrix, the matrix is a generalization. AI application matrix is also quite wide!
Numerical analysis of the main branches to develop efficient algorithms matrix calculation, which is a problem since centuries, is a growing area of research. Matrix decomposition approach simplifies theoretical and practical calculations. Tailored to the particular matrix structure (such as sparse matrix and near-diagonal matrix) algorithm to speed up the calculation in the finite element method and other calculations. Infinite matrix occur in the planet theory and atomic theory. A simple example is representative of an infinite matrix derivative function of the Taylor series of the matrix operator.
Matrix History
A long history of research matrix, and Latin square magic square in prehistoric years have been studied.
In mathematics, a matrix (the Matrix) is a rectangular array arranged in accordance with a complex or real number set, from the first matrix coefficients and constants of the equation constituted. This concept was first proposed by British mathematician Kelly 19th century. As a tool for solving linear equations, matrices are also not short history. Written in the first pre-Han "Nine Chapter Arithmetic" , the linear equations represents separating coefficient, which has been augmented matrix. In the elimination process, the use of a row by a non-zero real numbers, and other operational techniques subtracted from another line in a row, corresponding to elementary transformation matrix. But then I did not understand the matrix concept today, although it is formally identical with the existing matrix, but at the time only that the treatment as a standard linear equations.
Matrix officially as the object of study in mathematics appears, after studying the determinant developed. Logically, the concept of matrix prior to the determinant, but just the opposite in actual history. Japanese mathematician Guan and Xiao (1683) and one of the discoverers of calculus Gottfried Wilhelm Leibniz (1693) almost simultaneously established an independent determinant theory. Thereafter determinant as a tool for solving linear equations of progressive development. 1750, Gabriel Cramer found Cramer's rule.
The concept of matrix gradually formed in the 19th century. 1800s, Goss and William of Jordan established Gauss - elimination of Jordan. In 1844, German mathematician Gotthold Eisenstein (F.Eisenstein) discussed the "transformation" (matrix) and its product. In 1850, the British mathematician James Joseph Sylvester (James Joseph Sylvester) first use of the word matrix.
英国数学家阿瑟·凯利被公认为矩阵论的奠基人。他开始将矩阵作为独立的数学对象研究时，许多与矩阵有关的性质已经在行列式的研究中被发现了，这也使得凯利认为矩阵的引进是十分自然的。他说：“我决然不是通过四元数而获得矩阵概念的；它或是直接从行列式的概念而来，或是作为一个表达线性方程组的方便方法而来的。”他从1858年开始，发表了《矩阵论的研究报告》等一系列关于矩阵的专门论文，研究了矩阵的运算律、矩阵的逆以及转置和特征多项式方程。凯利还提出了凯莱-哈密尔顿定理，并验证了3×3矩阵的情况，又说进一步的证明是不必要的。哈密尔顿证明了4×4矩阵的情况，而一般情况下的证明是德国数学家弗罗贝尼乌斯（F.G.Frohenius）于1898年给出的 。
1854年时法国数学家埃尔米特（C.Hermite）使用了“正交矩阵”这一术语，但他的正式定义直到1878年才由费罗贝尼乌斯发表。1879年，费罗贝尼乌斯引入矩阵秩的概念。至此，矩阵的体系基本上建立起来了。
无限维矩阵的研究始于1884年。庞加莱在两篇不严谨地使用了无限维矩阵和行列式理论的文章后开始了对这一方面的专门研究。1906年，希尔伯特引入无限二次型（相当于无限维矩阵）对积分方程进行研究，极大地促进了无限维矩阵的研究。在此基础上，施密茨、赫林格和特普利茨发展出算子理论，而无限维矩阵成为了研究函数空间算子的有力工具 。
矩阵的概念最早在1922年见于中文。1922年，程廷熙在一篇介绍文章中将矩阵译为“纵横阵”。1925年，科学名词审查会算学名词审查组在《科学》第十卷第四期刊登的审定名词表中，矩阵被翻译为“矩阵式”，方块矩阵翻译为“方阵式”，而各类矩阵如“正交矩阵”、“伴随矩阵”中的“矩阵”则被翻译为“方阵”。1935年，中国数学会审查后，中华民国教育部审定的《数学名词》（并“通令全国各院校一律遵用，以昭划一”）中，“矩阵”作为译名首次出现。1938年，曹惠群在接受科学名词审查会委托就数学名词加以校订的《算学名词汇编》中，认为应当的译名是“长方阵”。中华人民共和国成立后编订的《数学名词》中，则将译名定为“（矩）阵”。1993年，中国自然科学名词审定委员会公布的《数学名词》中，“矩阵”被定为正式译名，并沿用至今。
学习AI离不开矩阵
矩阵对基本的一种数学算法，这些算法对AI意义重大！那么数学和AI的关系是什么呢？AI的本质就是计算机科学的一部分，它也需要借助大部分计算机的各种技术！当然，也需要用到软件，软件是由逻辑语言写成的，而任何逻辑语言都是离不开算法的，所以说，想要学好AI，那么一定要熟悉各种数学算法，其中就包括最常用到的矩阵！
如何学习矩阵
很多人在学习矩阵理论时，经常会感到非常吃力，觉得矩阵理论的逻辑符号十分繁琐，运算方法不易理解，定义定理很难掌握，最后导致学习的效率不高、效果不好。比如，实际中经常用到的是非负矩阵及其特征值和特征向量的性质，在教学的过程中，发现学生经常出现问题，经常搞混非负矩阵的分类以及它们的特征值的性质。出现的问题有：非负方阵是否有正特征值，如果有的话，是否惟一；是否有正的特征向量，如果有的话，是否惟一，等等。
其实，矩阵学习的第一步就是追根溯源，找到它的发展历史，在了解它的发展历史之后，我们学习矩阵来才会事倍功半！