On generalized quadratic matrices

被引：12

作者：

Farebrother, RW ^{[1
]}

Trenkler, G ^{[1
]}

机构：

[1] Univ Dortmund, Dept Stat, Fachbereich Stat, D-44221 Dortmund, Germany

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 410卷

关键词：

generalized quadratic matrices; idempotent matrix; eigenvalue; Moore-Penrose inverse; group inverse;

D O I：

10.1016/j.laa.2005.08.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper a wide class of matrices is considered, containing idempotent, involutory, nilpotent and several other types of matrices. Extending an approach considered by Radjavi and Rosenthal [H. Radjavi, P Rosenthal, On commutators of idempotents, Linear Multilinear Algebra 50 (2) (2002) 121-124], we investigate the set Q(P) of square matrices A is an element of C-nxn satisfying the equation A(2) = alpha A + beta A for some complex numbers alpha and beta and for some n x n nonzero complex idempotent matrix P such the AP = PA = A. Special attention is paid to the Moore-Penrose and group inverse of matrices belonging to 2(P). (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：244 / 253

页数：10

共 7 条

[1]

ALCKSIEJCZYK M, 2000, MATH PANNON, V11, P239

[2]

Ben-Israel A., 2003, GEN INVERSES THEORY, V15

[3]

Goldberg J. L., 1991, MATRIX THEORY APPL

[4] MAXIMAL ELEMENTS UNDER THE 3 PARTIAL ORDERS [J].

HARTWIG, RE ;

LOEWY, R .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 175 :39-61

[5]

Hartwig RE., 1983, LINEAR MULTILINEAR A, V13, P295

[6] On commutators of idempotents [J].

Radjavi, H ;

Rosenthal, P .

LINEAR & MULTILINEAR ALGEBRA, 2002, 50 (02) :121-124

[7]

RAO AR, 1992, LINEAR ALGEBRA

← 1 →