In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.
翻译：1954年,Alston S. Familyer出版了《数字分析原则》,这是在矩阵分解法上第一种现代处理办法,有利于(区块)LU分解,将一个矩阵分解成分解成下三角和上三角矩阵的产物,而现在,矩阵分解已成为机器学习的核心技术,这主要是因为在安装神经网络时开发了后传播算法,这一调查的唯一目的是在数字线性代数和矩阵分析中自成一体地介绍概念和数学工具,以便在随后的章节中无缝地引入矩阵分解技术及其应用。然而,我们清楚地认识到我们无法涵盖关于矩阵分解的所有有用和令人感兴趣的结果,而且考虑到讨论的范围很小,例如,对欧几里德空间、赫米蒂安空间、希尔伯特空间和复杂领域的事物的分别分析。我们请读者参考线性代数领域的文献,以便更详细地介绍相关领域。