Spectral and weak polynomial completeness for the product of nonsingular matrices

Detalhes bibliográficos
Autor(a) principal: Iglésias, Laura
Data de Publicação: 2015
Outros Autores: Silva, Fernando C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/6003
Resumo: Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).
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spelling Spectral and weak polynomial completeness for the product of nonsingular matricesEigenvaluesCharacteristic polynomialInvariant polynomialsFactorization of matricesLet F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).TAYLOR & FRANCIS LTDRCIPLIglésias, LauraSilva, Fernando C.2016-04-15T16:11:26Z2015-10-032015-10-03T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/6003engIGLÉSIAS, LAURA; SILVA, FERNANDO C.; - Spectral and weak polynomial completeness for the product of nonsingular matrices. Linear and Multilinear Algebra. ISSN.0308-1087. Vol. 63, N.º 10, SI (2015), pp. 1937-1946.0308-108710.1080/03081087.2013.862620metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T09:50:14Zoai:repositorio.ipl.pt:10400.21/6003Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:15:13.082458Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Spectral and weak polynomial completeness for the product of nonsingular matrices
title Spectral and weak polynomial completeness for the product of nonsingular matrices
spellingShingle Spectral and weak polynomial completeness for the product of nonsingular matrices
Iglésias, Laura
Eigenvalues
Characteristic polynomial
Invariant polynomials
Factorization of matrices
title_short Spectral and weak polynomial completeness for the product of nonsingular matrices
title_full Spectral and weak polynomial completeness for the product of nonsingular matrices
title_fullStr Spectral and weak polynomial completeness for the product of nonsingular matrices
title_full_unstemmed Spectral and weak polynomial completeness for the product of nonsingular matrices
title_sort Spectral and weak polynomial completeness for the product of nonsingular matrices
author Iglésias, Laura
author_facet Iglésias, Laura
Silva, Fernando C.
author_role author
author2 Silva, Fernando C.
author2_role author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Iglésias, Laura
Silva, Fernando C.
dc.subject.por.fl_str_mv Eigenvalues
Characteristic polynomial
Invariant polynomials
Factorization of matrices
topic Eigenvalues
Characteristic polynomial
Invariant polynomials
Factorization of matrices
description Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).
publishDate 2015
dc.date.none.fl_str_mv 2015-10-03
2015-10-03T00:00:00Z
2016-04-15T16:11:26Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.21/6003
url http://hdl.handle.net/10400.21/6003
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv IGLÉSIAS, LAURA; SILVA, FERNANDO C.; - Spectral and weak polynomial completeness for the product of nonsingular matrices. Linear and Multilinear Algebra. ISSN.0308-1087. Vol. 63, N.º 10, SI (2015), pp. 1937-1946.
0308-1087
10.1080/03081087.2013.862620
dc.rights.driver.fl_str_mv metadata only access
info:eu-repo/semantics/openAccess
rights_invalid_str_mv metadata only access
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv TAYLOR & FRANCIS LTD
publisher.none.fl_str_mv TAYLOR & FRANCIS LTD
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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