Symmetric Integer Matrices Having Integer Eigenvalues

Symmetric Integer Matrices Having Integer Eigenvalues

We provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and integer eigenvalue problem.

Bibliographic Details
Main Authors: Lei Cao, Selcuk Koyuncu
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2016/3471438
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spelling doaj-d014aad4933b47459f1b9435f93366532020-11-25T01:05:12ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252016-01-01201610.1155/2016/34714383471438Symmetric Integer Matrices Having Integer EigenvaluesLei Cao0Selcuk Koyuncu1Department of Mathematics, Georgian Court University, Lakewood, NJ 08701, USADepartment of Mathematics, University of North Georgia, Gainesville, GA 30566, USAWe provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and integer eigenvalue problem.http://dx.doi.org/10.1155/2016/3471438
collection DOAJ
language English
format Article
sources DOAJ
author Lei Cao
Selcuk Koyuncu
spellingShingle Lei Cao
Selcuk Koyuncu
Symmetric Integer Matrices Having Integer Eigenvalues
International Journal of Mathematics and Mathematical Sciences
author_facet Lei Cao
Selcuk Koyuncu
author_sort Lei Cao
title Symmetric Integer Matrices Having Integer Eigenvalues
title_short Symmetric Integer Matrices Having Integer Eigenvalues
title_full Symmetric Integer Matrices Having Integer Eigenvalues
title_fullStr Symmetric Integer Matrices Having Integer Eigenvalues
title_full_unstemmed Symmetric Integer Matrices Having Integer Eigenvalues
title_sort symmetric integer matrices having integer eigenvalues
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2016-01-01
description We provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and integer eigenvalue problem.
url http://dx.doi.org/10.1155/2016/3471438
work_keys_str_mv AT leicao symmetricintegermatriceshavingintegereigenvalues
AT selcukkoyuncu symmetricintegermatriceshavingintegereigenvalues
_version_ 1725195625481371648

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