矩阵因子分解及其应用举例  

Matrix Factors with Applications

作　　者：王文杰 梁卓滨 WANG Wen-jie;LIANG Zhuo-bin(College of Information Science and Technology, Jinan University,Guangzhou 510632, China)

机构地区：[1]暨南大学信息科学技术学院,广州510632

出　　处：《大学数学》2020年第4期111-116,共6页College Mathematics

基　　金：暨南大学青年培育基金(21615135)。

摘　　要：通过矩阵方程定义了矩阵的左、右因子和双因子,给出了各类因子存在的充要条件,并将其应用到满秩分解和极分解等典型例子中.论证中,采用多种观点和方法,空间映射、矩阵运算并重.Three types of matrix factors(left,right and double factors)are defined by means of matrix equations,and then the necessary and sufficient conditions for the existence of matrix factors are given.Examples such as full rank decomposition,polar decomposition etc.are provided to demonstrate the application of matrix factors.Various viewpoints and methods,with equal emphasis on techniques of space mapping and matrix operation,are exploited in the proofs.

关 键 词：矩阵因子 直和 线性同构 极分解 

分 类 号：O151.2[理学—数学]