Lower bounds in minimum rank problems

被引：18
|
作者：
Mitchell, Lon H. [1 ]
Narayan, Sivaram K. [2 ]
Zimmer, Andrew M. [3 ]
机构：
[1] Virginia Commonwealth Univ, Dept Math, Richmond, VA 23284 USA
[2] Cent Michigan Univ, Dept Math, Mt Pleasant, MI 48859 USA
[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 432卷 / 01期
关键词：
Minimum rank; Minimum semidefinite rank; Zero forcing set; GRAPHS; REPRESENTATIONS; MATRICES;
D O I：
10.1016/j.laa.2009.08.023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the given graph. The minimum semidefinite rank of a graph is the minimum rank among Hermitian positive semidefinite matrices with the given graph. We explore connections between OS-sets and a lower bound for minimum rank related to zero forcing sets as well as exhibit graphs for which the difference between the minimum semidefinite rank and these lower bounds can be arbitrarily large. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：430 / 440
页数：11
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