Matrices A such that AA† - A†A are nonsingular

被引：21

作者：

Benitez, Julio ^{[1
]}

Rakocevic, Vladimir ^{[2
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Dept Matemat Aplicada, Valencia 46022, Spain

[2] Univ Nis, Fac Sci & Math, Dept Math, Nish 18000, Serbia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 07期

关键词：

Co-EP matrices; Moore-Penrose inverse; Idempotent; Orthogonal projectors; CS DECOMPOSITION; EP MATRICES; IDEMPOTENTS; PROJECTIONS; DIFFERENCE; SPACE; INVERTIBILITY; SUBSPACES; ANGLES; SUMS;

D O I：

10.1016/j.amc.2010.09.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the class of square matrices A such that AA(dagger) - A(dagger)A is nonsingular, where A(dagger) stands for the Moore-Penrose inverse of A. Among several characterizations we prove that for a matrix A of order n, the difference AA(dagger) - A(dagger)A is nonsingular if and only if R(A) circle plus R(A*) = C-n,C-1, where R(.) denotes the range space. Also we study matrices A such that R(A)(perpendicular to) = R(A*). (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3493 / 3503

页数：11

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