矩阵的分解及其应用研究 摘 要数学是一门重要的基础学科，也是一门重要的应用学科，矩阵则是数学体系中占据关键位置的常用工具。矩阵的分解给矩阵的简便运算提供了可能，有利于矩阵在数学领域中的应用，也促进了矩阵在物理学、光学、力学、计算机科学、图像研究等方面的应用有了质的飞跃。本文从多维度出发，系统的总结了矩阵分解的方法及应用，并对非负矩阵这种特殊矩阵的分解及应用进行了分析，以期通过本文的研究，将矩阵分解的应用更系统化的展现出来。关键词：矩阵；矩阵分解；非负矩阵分解；应用IMatrix decomposition and its application researchAbstractMathematics is an important basic subject, is also an important application of the subject, in the matrix is a mathematical system occupies the key position of the commonly used tools. Matrix decomposition gives the simple operation of the matrix, matrix application in the field of mathematics, also contributed to the matrix in physics, optics, mechanics, computer science, image study applied a qualitative leap. Based on multi-dimensional, this paper summarizes the method of matrix decomposition and the application of the system, and the decomposition of this special matrix of nonnegative matrices and application are analyzed, in order to through the study of this article, the application of matrix decomposition is more systematic.Keywords: matrix; matrix decomposition; nonnegative matrix decomposition; applicationII目 录1 引言.......................................................................11.1 研究背景及意义..........................................................11.2 研究概况................................................................12 矩阵分解的理论和方法概述...................................................12.1 矩阵的概念..............................................................12.2 矩阵分解的内涵和方法....................................................22.2.1 矩阵分解的和形式.........................
