Invariance properties of a triple matrix product involving generalized inverses

被引：19

作者：

Gross, Juergen ^{[1
]}

Tian, Yongge

机构：

[1] Univ Dortmund, Dept Stat, D-44225 Dortmund, Germany

[2] Shanghai Univ Finance & Econ, Sch Econ, Shanghai 200433, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 417卷 / 01期

关键词：

generalized inverse; Moore-Penrose inverse; rank; range; partitioned matrix;

D O I：

10.1016/j.laa.2006.03.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given complex-valued matrices A, B and C of appropriate dimensions, this paper investigates certain invariance properties of the product AXC with respect to the choice of X, where X is a generalized inverse of B. Different types of generalized inverses are taken into account. The purpose of the paper is three-fold: First, to review known results scattered in the literature, second, to demonstrate the connection between invariance properties and the concept of extremal ranks of matrices, and third, to add new results related to the topic. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：94 / 107

页数：14

共 16 条

[1]

[Anonymous], 1971, GEN INVERSES MATRICE

[2]

Baksalary J.K., 1983, LINEAR MULTILINEAR A, V14, P89

[3] Further results on invariance of the eigenvalues of matrix products involving generalized inverses [J].