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Nonsparse Companion Hessenberg Matrices

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dc.contributor.authorBorobia Vizmanos, Alberto
dc.contributor.authorCanogar Mckenzie, Roberto
dc.contributor.funderMinisterio de Ciencia, Innovación y Universidades. España
dc.date.accessioned2025-12-05T16:32:03Z
dc.date.available2025-12-05T16:32:03Z
dc.date.issued2021-03-05
dc.descriptionThe registered version of this article, first published in Electronic Journal of Linear Algebra, is available online at the publisher's website: International Linear Algebra Society (ILAS), https://doi.org/10.13001/ela.2021.5405
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en Electronic Journal of Linear Algebra, está disponible en línea en el sitio web del editor: International Linear Algebra Society (ILAS), https://doi.org/10.13001/ela.2021.5405
dc.description.abstractIn recent years, there has been a growing interest in companion matrices. Sparse companion matrices are well known: every sparse companion matrix is equivalent to a Hessenberg matrix of a particular simple type. Recently, Deaett et al. [Electron. J. Linear Algebra, 35:223247, 2019] started the systematic study of nonsparse companion matrices. They proved that every nonsparse companion matrix is nonderogatory, although not necessarily equivalent to a Hessenberg matrix. In this paper, the nonsparse companion matrices which are unit Hessenberg are described. In a companion matrix, the variables are the coordinates of the characteristic polynomial with respect to the monomial basis. A PB-companion matrix is a generalization, in the sense that the variables are the coordinates of the characteristic polynomial with respect to a general polynomial basis. The literature provides examples with Newton basis, Chebyshev basis, and other general orthogonal bases. Here, the PB-companion matrices which are unit Hessenberg are also described.en
dc.description.provenanceMade available in DSpace on 2025-12-05T16:32:03Z (GMT). No. of bitstreams: 1 Nonsparse.pdf: 438510 bytes, checksum: f000a030320f052e7272b59589f597cb (MD5) Previous issue date: 2021-03-05en
dc.description.sponsorshipProyecto financiado por la Agencia Estatal de Investigación de España (PID2019106362GB-I00/AEI/10.13039/501100011033) y (MTM2017-90682-REDT).
dc.description.versionversión publicada
dc.identifier.citationBorobia, A., & Canogar, R. (2021). Nonsparse companion hessenberg matrices. Electronic Journal of Linear Algebra, 37, 193-210. https://doi.org/10.13001/ELA.2021.5405
dc.identifier.doihttps://doi.org/10.13001/ela.2021.5405
dc.identifier.issn1537-9582
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31037
dc.journal.titleElectronic Journal of Linear Algebra
dc.journal.volume37
dc.language.isoen
dc.page.final210
dc.page.initial193
dc.publisherInternational Linear Algebra Society (ILAS)
dc.relation.centerFacultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.relation.projectidinfo:eu-repo/grantAgreement/MICINN/Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad/PID2019106362GB-I00
dc.relation.projectidinfo:eu-repo/grantAgreement/MICINN/Redes de Excelencia del Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad/MTM2017-90682-REDT
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsCompanion matrixen
dc.subject.keywordsCharacteristic polynomialen
dc.subject.keywordsHessenberg matrixen
dc.subject.keywordsPolynomial basises
dc.subject.keywordsNilpotent matrixes
dc.titleNonsparse Companion Hessenberg Matricesen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublicationfda35eed-831c-4588-9504-f202a8c957f6
relation.isAuthorOfPublication6222b7d3-ae1d-411e-914a-a59610f0a254
relation.isAuthorOfPublication.latestForDiscoveryfda35eed-831c-4588-9504-f202a8c957f6
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