The number of 2x2 integer matrices having a prescribed integer eigenvalue

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dc.creatorMartin, Greg
dc.creatorWong, Erick B.
dc.date2008-08-14
dc.date.accessioned2026-07-07T09:56:38Z
dc.date.available2026-07-07T09:56:38Z
dc.descriptionRandom matrices arise in many mathematical contexts, and it is natural to ask about the properties that such matrices satisfy. If we choose a matrix with integer entries at random, for example, what is the probability that it will have a particular integer as an eigenvalue, or an integer eigenvalue at all? If we choose a matrix with real entries at random, what is the probability that it will have a real eigenvalue in a particular interval? The purpose of this paper is to resolve these questions, once they are made suitably precise, in the setting of 2x2 matrices.
dc.description18 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0808.1922
dc.identifierhttp://arxiv.org/abs/0808.1922
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167044
dc.subjectProbability
dc.subjectNumber Theory
dc.subject15A36, 15A52 (Primary) 11C20, 15A18, 60C05 (Secondary)
dc.titleThe number of 2x2 integer matrices having a prescribed integer eigenvalue
dc.typetext

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