Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns Hentzel, Irvin DeAlba, Luz Hardy, Timothy Hentzel, Irvin Hogben, Leslie Hogben, Leslie Wangsness, Amy
dc.contributor.department Mathematics 2018-02-18T06:08:57.000 2020-06-30T06:00:57Z 2020-06-30T06:00:57Z Sun Jan 01 00:00:00 UTC 2006 2006-10-01
dc.description.abstract <p>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.</p>
dc.description.comments <p>This is a manuscript of an article from <em>Linear Algebra and its Applications </em>418 (2006): 394, doi:<a href="" target="_blank">10.1016/j.laa.2006.02.018</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 1087
dc.identifier.contextkey 9890812
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/80
dc.language.iso en
dc.source.bitstream archive/|||Sat Jan 15 02:04:46 UTC 2022
dc.source.uri 10.1016/j.laa.2006.02.018
dc.subject.disciplines Algebra
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.keywords Sign pattern matrix
dc.subject.keywords Symmetric tree sign pattern
dc.subject.keywords Minimum rank
dc.subject.keywords Maximum multiplicity
dc.subject.keywords Tree
dc.subject.keywords Graph
dc.title Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication 70506428-9d7c-4c43-bcfa-d89bbb2149e4
relation.isAuthorOfPublication 0131698a-00df-41ad-8919-35fb630b282b
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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