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A note on the rational canonical form of an endomorphism of a vector space of finite dimensions

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A note on the rational canonical form of an endomorphism of a vector space of finite dimensions

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dc.contributor.author Ballester-Bolinches, A. es_ES
dc.contributor.author Esteban Romero, Ramón es_ES
dc.contributor.author Pérez-Calabuig, Vicente es_ES
dc.date.accessioned 2020-06-11T03:33:55Z
dc.date.available 2020-06-11T03:33:55Z
dc.date.issued 2018 es_ES
dc.identifier.issn 1846-3886 es_ES
dc.identifier.uri http://hdl.handle.net/10251/146002
dc.description.abstract [EN] In this note, we give an easy algorithm to construct the rational canonical form of a square matrix or an endomorphism h of a finite dimensional vector space which does not depend on either the structure theorem for finitely generated modules over principal ideal domains or matrices over the polynomial ring. The algorithm is based on the construction of an element whose minimum polynomial coincides with the minimum polynomial of the endomorphism and on the fact that the h-invariant subspace generated by such an element admits an h-invariant complement. It is also shown that this element can be easily obtained without the factorisation of a polynomial as a product of irreducible polynomials. es_ES
dc.description.sponsorship This work has been supported by the grants MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union, and PROMETEO/2017/057 from the Generalitat (Valencian Community, Spain). The first author has been also supported by a project from the National Natural Science Foundation of China (NSFC, No. 11271085) and a project of Natural Science Foundation of Guangdong Province, China (No. 2015A030313791). The third author has been also supported by a predoctoral grant from the programme Atracció del talent of the Universitat de València.
dc.language Inglés es_ES
dc.publisher Element d.o.o. es_ES
dc.relation.ispartof Operators and Matrices es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Similarity of matrices es_ES
dc.subject Rational canonical form es_ES
dc.subject Minimum polynomial es_ES
dc.subject Endomorphism es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A note on the rational canonical form of an endomorphism of a vector space of finite dimensions es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.7153/oam-2018-12-49 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/Natural Science Foundation of Guangdong Province//2015A030313791/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F057/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSFC//11271085/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2014-54707-C3-1-P/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE GRUPOS Y SEMIGRUPOS I/ es_ES
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Ballester-Bolinches, A.; Esteban Romero, R.; Pérez-Calabuig, V. (2018). A note on the rational canonical form of an endomorphism of a vector space of finite dimensions. Operators and Matrices. 12(3):823-836. https://doi.org/10.7153/oam-2018-12-49 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.7153/oam-2018-12-49 es_ES
dc.description.upvformatpinicio 823 es_ES
dc.description.upvformatpfin 836 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 12 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\376466 es_ES
dc.contributor.funder Ministerio de Economía y Competitividad
dc.contributor.funder European Commission
dc.contributor.funder European Regional Development Fund
dc.contributor.funder Generalitat Valenciana
dc.contributor.funder National Natural Science Foundation of China
dc.contributor.funder Natural Science Foundation of Guangdong Province
dc.contributor.funder Universitat de València


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