Flanders' theorem for many matrices under commutativity assumptions

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dc.contributor.author Teran Vergara, Fernando de
dc.contributor.author Lippert, Ross A.
dc.contributor.author Nakatsukasa, Yuji
dc.contributor.author Noferini, Vanni
dc.date.accessioned 2015-12-11T08:33:41Z
dc.date.issued 2014-02-15
dc.identifier.bibliographicCitation Linear Algebra Appl 443 (2014) 15 February, pp.120-138
dc.identifier.issn 0024-3795
dc.identifier.uri http://hdl.handle.net/10016/22081
dc.description.abstract We analyze the relationship between the Jordan canonical form of products, in different orders, of k square matrices A1,.,Ak. Our results extend some classical results by H. Flanders. Motivated by a generalization of Fiedler matrices, we study permuted products of A1,.,Ak under the assumption that the graph of non-commutativity relations of A1,.,Ak is a forest. Under this condition, we show that the Jordan structure of all nonzero eigenvalues is the same for all permuted products. For the eigenvalue zero, we obtain an upper bound on the difference between the sizes of Jordan blocks for any two permuted products, and we show that this bound is attainable. For k=3 we show that, moreover, the bound is exhaustive.
dc.description.sponsorship This research has been sSupported by the Ministerio de Economía y Competitividad of Spain through grants MTM-2009-09281 and MTM-2012-32542.
dc.format.extent 24
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2014 Elsevier
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Cut-flip
dc.subject.other Eigenvalue
dc.subject.other Flanders' theorem
dc.subject.other Forest
dc.subject.other Jordan canonical form
dc.subject.other Permuted products
dc.subject.other Product of matrices
dc.subject.other Segré characteristic
dc.subject.other Cut-flip
dc.subject.other Forestry
dc.subject.other Eigenvalues and eigenfunctions
dc.title Flanders' theorem for many matrices under commutativity assumptions
dc.type article
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1016/j.laa.2013.11.026
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/j.laa.2013.11.026
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM-2012-32542
dc.relation.projectID Gobierno de España. MTM-2009-09281
dc.type.version submittedVersion
dc.identifier.publicationfirstpage 120
dc.identifier.publicationlastpage 138
dc.identifier.publicationtitle Linear Algebra and its Applications
dc.identifier.publicationvolume 443
dc.identifier.uxxi AR/0000014550
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