Generalized inverses and a block-rank equation

被引：29

作者：

Thome, M

Wei, Y ^{[1
]}

机构：

[1] Fudan Univ, Dept Math, Shanghai 200433, Peoples R China

[2] Univ Politecn Valencia, Dept Matemat Aplicada, E-46071 Valencia, Spain

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2003年 / 141卷 / 2-3期

基金：

中国国家自然科学基金;

关键词：

rank equation; group inverse; jordan canonical form; reflexive generalized inverse;

D O I：

10.1016/S0096-3003(02)00268-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a square matrix A of index 1, the block-rank equation rank [(A)(C) (B)(X)] = rank(A) is studied. Geometrical conditions are given to characterize the solution of this equation. Further, all matrices B and C are described for the solution X = A(#), where A(#) is the group inverse of A. In addition, we extend these results to reflexive generalized inverses. This contributes to a result recently obtained by Wei [SIAM J. Matrix Anal. Appl. 17 (1996) 7441 and it is a generalization of a result by Gross [Lin. Alg. Appl. 289 (1999) 127]. (C) 2002 Elsevier Science Inc. All rights reserved.

引用

页码：471 / 476

页数：6

共 13 条

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[2]

BENISRAEL A, 1974, GEN INVERSES THEORY

[3]

BRAND L, 1962, MATH GAZ, V46, P203

[4]

Bru R., 1998, Linear Multilinear Algebra, V45, P207