A note on the Drazin inverses with Banachiewicz-Schur forms

被引：27

作者：

Deng, Chun Yuan ^{[1
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 213卷 / 01期

关键词：

Banachiewicz-Schur form; Generalized inverse; Generalized Schur complement; Drazin inverse; Moore-Penrose inverse; EP-operator;

D O I：

10.1016/j.amc.2009.03.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let H be a Hilbert space, M the closed subspace of H with orthocomplement M-1. According to the orthogonal decomposition H = M circle plus M-perpendicular to, every operator M is an element of B (H) can be written in a block-form [GRAPHICS] . In this note, we give necessary and sufficient conditions for a partitioned operator matrix M to have the Drazin inverse with Banachiewicz-Schur form. In addition, this paper investigates the relations among the Drazin inverse, the Moore-Penrose inverse and the group inverse when they can be expressed in the Banachiewicz-Schur forms. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：230 / 234

页数：5

共 12 条

[1] Properties of Schur complements in partitioned idempotent matrices [J].

Baksalary, JK ;

Baksalary, OM ;

Szulc, T .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 379 :303-318

[2] Generalized inverses of partitioned matrices in Banachiewicz-Schur form [J].

Baksalary, JK ;

Styan, GPH .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 354 (1-3) :41-47

[3]

Ben-Israel A., 2003, Generalized inverses: theory and applications

[4] The generalized Schur complement in group inverses and (k+1)-potent matrices [J].

Benitez, Julio ;

Thome, Nestor .

LINEAR & MULTILINEAR ALGEBRA, 2006, 54 (06) :405-413

[5]

CAMPBELL SL, 1979, GEN INVERSE LINEAR T

[6] Additive results for the generalized Drazin inverse [J].

Djordjevic, DS ;

Wei, YM .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2002, 73 :115-125

[7] On the generalized Drazin inverse and generalized resolvent [J].

Djordjevic, DS ;

Stanimirovic, PS .

CZECHOSLOVAK MATHEMATICAL JOURNAL, 2001, 51 (03) :617-634

[8] Representations for the Drazin inverse of a 2 x 2 block matrix [J].

Hartwig, R ;

Li, XZ ;

Wei, YM .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2005, 27 (03) :757-771

[9] A note on the representations for the Drazin inverse of 2x2 block matrices [J].

Li, Xiezhang ;

Wei, Yimin .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 423 (2-3) :332-338

[10]

Wei Y., 1998, LINEAR MULTILINEAR A, V45, P131

← 1 2 →