Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

10-2006

Journal or Book Title

Linear Algebra and its Applications

Volume

418

DOI

10.1016/j.laa.2006.02.017

Abstract

A sign pattern is a matrix whose entries are elements of {+, −, 0}; it describes the set of real matrices whose entries have the signs in the pattern. A graph (that allows loops but not multiple edges) describes the set of symmetric matrices having a zero-nonzero pattern of entries determined by the absence or presence of edges in the graph. DeAlba et al. [L.M. DeAlba, T.L. Hardy, I.R. Hentzel, L. Hogben, A. Wangsness, Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns, Linear Algebra Appl., in press, doi:10.1016/j.laa.2006.02.018.] gave algorithms for the computation of maximum multiplicity and minimum rank of matrices associated with a tree sign pattern or tree, and an algorithm to obtain an integer matrix realizing minimum rank. We extend these results by giving algorithms to obtain a symmetric rational matrix realizing the maximum multiplicity of a rational eigenvalue among symmetric matrices associated with a symmetric tree sign pattern or tree.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 418 (2006): 380, doi:10.1016/j.laa.2006.02.017. 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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