矩阵乘积的加权最小二乘广义逆的反序律研究  

On Reverse Order Laws for the Weighted Least Square Generalized Inverses of Matrix Products

作　　者：邱柏凤 熊志平[1] QIU Bai-feng;XIONG Zhi-ping(School of Mathematics and Computational Science,Wuyi University,Jiangmen 529020,China)

机构地区：[1]五邑大学数学与计算科学学院,广东江门529020

出　　处：《五邑大学学报（自然科学版）》2023年第4期13-17,共5页Journal of Wuyi University(Natural Science Edition)

基　　金：2021年度广东省教育厅省级课程思政示范项目(DSZ2021009);2022年广东省大学生创新训练项目(202211349312);2020年五邑大学课程思政建设改革示范项目(邑大教[2021]53号)。

摘　　要：加权广义逆是矩阵理论与应用中不可或缺的一部分,它在线性偏微分方程、多元统计分析、线性控制理论等领域有着广泛的应用.本文利用广义Schur补的极大极小秩这一方法研究了一些矩阵乘积的加权广义逆的反序律,给出了矩阵乘积的加权广义逆的反序律A_(3){1,3M_(3)}A_(2){1,3M_(2)}A_(1){1,3M_(1)}■(A_(1)A_(2)A_(3)){1,3M_(1)} 和 A_(3){1, 4M_(4)}A_(2){1, 4M_(3)}A_(1){1, 4M_(2)}■(A_(1)A_(2)A_(3)){1,4M_(4)}成立的充分必要条件.The weighted generalized inverse is an indispensable part of the matrix theory and its application,which is widely used in linear partial differential equations,multivariate statistical analysis,the linear control theory and other fields.In this paper,we study the reverse order laws for the weighted generalized inverses of matrix products by using the maximal and minimal ranks of the generalized Schur complement.The necessary and sufficient conditions for the reverse order laws A_(3){1,3M_(3)}A_(2){1,3M_(2)}A_(1){1,3M_(1)}■(A_(1)A_(2)A_(3)){1,3M_(1)} and A_(3){1, 4M_(4)}A_(2){1, 4M_(3)}A_(1){1, 4M_(2)}■(A_(1)A_(2)A_(3)){1,4M_(4)} are obtained.

关 键 词：加权最小二乘广义逆 反序律 广义SCHUR补 秩等式 秩不等式 

分 类 号：O151.21[理学—数学]