On a matrix decomposition of Hartwig and Spindelbock

被引：47

作者：

Baksalary, Oskar Maria ^{[1
,3
]}

Styan, George P. H. ^{[2
]}

Trenkler, Goetz ^{[1
]}

机构：

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

[2] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

[3] Adam Mickiewicz Univ Poznan, Fac Phys, PL-61614 Poznan, Poland

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 10期

关键词：

Group inverse; Moore-Penrose inverse; g-Inverse; Drazin inverse; GP matrix; EP matrix; Partial isometry; Star-dagger matrix; Idempotent matrix; Projector; Quadripotent matrix; Core matrix; Noncore matrix; Star partial ordering; Sharp partial ordering; Minus partial ordering; PARTIAL ORDER; PROJECTORS; INVERSES; EP;

D O I：

10.1016/j.laa.2009.01.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main task of the paper is to demonstrate that Corollary 6 in [R.E. Hartwig, K. Spindelbock, Matrices for which A* and A(dagger) commute, Linear and Multilinear Algebra 14 (1984) 241-256] provides a powerful tool to investigate square matrices with complex entries. This aim is achieved, on the one hand, by obtaining several original results involving square matrices, and, on the other hand, by reestablishing some of the facts already known in the literature, often in extended and/or generalized forms. The particular attention is paid to the usefulness of the aforementioned corollary to characterize various classes of matrices and to explore matrix partial orderings. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2798 / 2812

页数：15

共 29 条

[1] CONDITIONS FOR POSITIVE AND NONNEGATIVE DEFINITENESS IN TERMS OF PSEUDOINVERSES [J].