Graphical description of group inverses of certain bipartite matrices

被引：13

作者：

Catral, M. ^{[2
]}

Olesky, D. D. ^{[1
]}

van den Driessche, P. ^{[2
]}

机构：

[1] Univ Victoria, Dept Comp Sci, Victoria, BC V8W 3P6, Canada

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P6, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 432卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Group inverse; Bipartite matrix; Broom graph; Signed group inverse;

D O I：

10.1016/j.laa.2009.07.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A necessary and sufficient condition for the existence of the group inverse of a certain bipartite matrix is given, and an explicit formula is obtained for the group inverse in terms of its block submatrices. This form is used to derive a graph-theoretic description of the entries of the group inverse of some examples of such a matrix, including those corresponding to broom graphs. If the group inverse of a nonnegative matrix corresponding to a broom graph exists, then it is shown that this group inverse is signed. An open question about group inverses of more general bipartite matrices is posed and a summary of cases for which its answer is known is given. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：36 / 52

页数：17

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