Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

10-2006

Journal or Book Title

Linear Algebra and its Applications

Volume

418

DOI

10.1016/j.laa.2006.02.018

Abstract

The set of real matrices described by a sign pattern (a matrix whose entries are elements of {+, −, 0}) has been studied extensively but only loose bounds were available for the minimum rank of a tree sign pattern. A simple graph has been associated with the set of symmetric matrices having a zero–nonzero pattern of off-diagonal entries described by the graph, and the minimum rank/maximum eigenvalue multiplicity among matrices in this set is readily computable for a tree. In this paper, we extend techniques for trees to tree sign patterns and trees allowing loops (with the presence or absence of loops describing the zero–nonzero pattern of the diagonal), allowing precise computation of the minimum rank of a tree sign pattern and a tree allowing loops. For a symmetric tree sign pattern or a tree that allows loops, we provide an algorithm that allows exact computation of maximum multiplicity and minimum rank, and can be used to obtain a symmetric integer matrix realizing minimum rank.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 418 (2006): 394, doi:10.1016/j.laa.2006.02.018. Posted with permission.

Rights

This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Published Version

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