On ranks of matrices associated with trees

被引：10

作者：

Chen, GT ^{[1
]}

Hall, FJ

Li, ZS

Wei, B

机构：

[1] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

[2] Univ Mississippi, Dept Math, University, MS 38677 USA

来源：

GRAPHS AND COMBINATORICS | 2003年 / 19卷 / 03期

关键词：

sign pattern matrix; symmetric tree sign pattern; minimal rank; symmetric minimal rank;

D O I：

10.1007/s00373-002-0522-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A sign pattern matrix is a matrix whose entries are from the set {+, -0}. The purpose of this paper is to obtain bounds on the minimum rank of any symmetric sign pattern matrix A whose graph is a free T (possibly with loops). In the special case when A is nonnegative with positive diagonal and the graph of A is "star-like", the exact value of the minimum rank of A is obtained. As a result, it is shown that the gap between the symmetric minimal and maximal ranks can be arbitrarily large for a symmetric tree sign pattern A.

引用

页码：323 / 334

页数：12

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