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On bundles of matrix pencils under strict equivalence

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señaleses
dc.contributor.authorTerán Vergara, Fernando de
dc.contributor.authorMartínez Dopico, Froilán César
dc.contributor.funderComunidad de Madrides
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.contributor.funderUniversidad Carlos III de Madrides
dc.date.accessioned2023-02-24T12:45:17Z
dc.date.available2023-02-24T12:45:17Z
dc.date.issued2023-02-01
dc.description.abstractBundles of matrix pencils (under strict equivalence) are sets of pencils having the same Kronecker canonical form, up to the eigenvalues (namely, they are an infinite union of orbits under strict equivalence). The notion of bundle for matrix pencils was introduced in the 1990's, following the same notion for matrices under similarity, introduced by Arnold in 1971, and it has been extensively used since then. Despite the amount of literature devoted to describing the topology of bundles of matrix pencils, some relevant questions remain still open in this context. For example, the following two: (a) provide a characterization for the inclusion relation between the closures (in the standard topology) of bundles; and (b) are the bundles open in their closure? The main goal of this paper is providing an explicit answer to these two questions. In order to get this answer, we also review and/or formalize some notions and results already existing in the literature. We also prove that bundles of matrices under similarity, as well as bundles of matrix polynomials (defined as the set of m x n matrix polynomials of the same grade having the same spectral information, up to the eigenvalues) are open in their closure.en
dc.description.sponsorshipThis work has been supported by the Agencia Estatal de Investigación of Spain through grants PID2019-106362GB-I00 MCIN/ AEI/10.13039/501100011033/ and MTM2017-90682-REDT, and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).en
dc.format.extent31
dc.identifier.bibliographicCitationDe Terán, F., & Dopico, F. M. (2023). On bundles of matrix pencils under strict equivalence. Linear Algebra and its Applications, 658, 1-31.en
dc.identifier.doihttps://doi.org/10.1016/j.laa.2022.10.029
dc.identifier.issn0024-3795
dc.identifier.publicationfirstpage1
dc.identifier.publicationlastpage31
dc.identifier.publicationtitleLinear Algebra and its Applicationsen
dc.identifier.publicationvolume658
dc.identifier.urihttps://hdl.handle.net/10016/36669
dc.identifier.uxxiAR/0000032130
dc.language.isoeng
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. PID2019-106362GB-I00es
dc.relation.projectIDComunidad de Madrid. EPUC3M23es
dc.relation.projectIDGobierno de España. MTM2017-90682-REDTes
dc.relation.projectIDAT-2022
dc.rights© 2022 The Author(s).en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherMatrixen
dc.subject.otherMatrix pencilen
dc.subject.otherMatrix polynomialen
dc.subject.otherSpectral informationen
dc.subject.otherStrict equivalenceen
dc.subject.otherKronecker canonical formen
dc.subject.otherJordan canonical formen
dc.subject.otherOrbiten
dc.subject.otherBundleen
dc.subject.otherOpen seten
dc.subject.otherClosureen
dc.subject.otherMajorizationen
dc.titleOn bundles of matrix pencils under strict equivalenceen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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