Group inverses of matrices with path graphs

被引：0
|
作者：
Catral, M. [1 ]
Olesky, D. D. [2 ]
Van den Driessche, P. [1 ]
机构：
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
[2] Univ Victoria, Dept Comp Sci, Victoria, BC V8W 3P6, Canada
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2008年 / 17卷
关键词：
group inverse; tridiagonal matrix; tree graph; Moore-Penrose inverse; bipartite digraph;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A simple formula for the group inverse of a 2 x 2 block matrix with a bipartite digraph is given in terms of the block matrices. This formula is used to give a graph-theoretic description of the group inverse of an irreducible tridiagonal matrix of odd order with zero diagonal ( which is singular). Relations between the zero/nonzero structures of the group inverse and the Moore-Penrose inverse of such matrices are given. An extension of the graph-theoretic description of the group inverse to singular matrices with tree graphs is conjectured.
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页码：219 / 233
页数：15
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