Relationships between generalized inverses of a matrix and generalized inverses of its rank-one-modifications

被引：4

作者：

Baksalary, JK

Baksalary, OM

机构：

[1] Zielona Gora Univ, Inst Math, PL-65246 Zielona Gora, Poland

[2] Adam Mickiewicz Univ, Inst Phys, PL-61614 Poznan, Poland

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2004年 / 388卷

关键词：

modified matrix; generalized inverse; reflexive generalized inverse;

D O I：

10.1016/j.laa.2004.03.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For given complex matrix A and nonzero complex vectors b, c, relationships between generalized inverses of A and generalized inverses of the rank-one-modified matrix M = A + bc* (with c* being the conjugate transpose of c) are investigated. The following three questions are considered: (i) when a given generalized inverse A(-) belongs to the set M{1} of all generalized inverses of M, (ii) when does A(-) epsilon A{1} exist such that simultaneously A(-) epsilon M{1}, and (iii) when the set A{1} is a subset of M{1}. The same questions are also discussed for reflexive generalized inverses of A and M. The answers obtained are commented from the view-point of a result concerning comparison of ranks of M and A. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：31 / 44

页数：14