On the Eigenvectors of Generalized Circulant Matrices

Detalhes bibliográficos
Autor(a) principal: Andrade, Enide
Data de Publicação: 2024
Outros Autores: Carrasco-Olivera, Dante, Manzaneda, Cristina
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/39946
Resumo: In \cite{Mourad}, Kaddoura and Mourad, in order to widen the scope of the class of circulant matrices, (see \cite{Davis}), constructed circulant-like matrices that were called generalized weighted circulant matrices. These matrices form a class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. The characteristic polynomials, eigenvalues and eigenvectors of the generalized permutation matrices corresponding to a family of permutations were described. Additionally, the eigenvalues of the weighted circulant matrices were given. However, their eigenvectors were not studied. Having these results as motivation, we present, in some cases, explicit formulas for the eigenvectors of the generalized weighted circulant matrices. In this work, they are simply called generalized circulant matrices.
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spelling On the Eigenvectors of Generalized Circulant MatricesCirculant matrixPermutation matrixGeneralized circulant matrixEigenvectorIn \cite{Mourad}, Kaddoura and Mourad, in order to widen the scope of the class of circulant matrices, (see \cite{Davis}), constructed circulant-like matrices that were called generalized weighted circulant matrices. These matrices form a class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. The characteristic polynomials, eigenvalues and eigenvectors of the generalized permutation matrices corresponding to a family of permutations were described. Additionally, the eigenvalues of the weighted circulant matrices were given. However, their eigenvectors were not studied. Having these results as motivation, we present, in some cases, explicit formulas for the eigenvectors of the generalized weighted circulant matrices. In this work, they are simply called generalized circulant matrices.Taylor & Francis2026-01-01T00:00:00Z2024-01-01T00:00:00Z2024info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/39946eng0308-108710.1080/03081087.2023.2284750Andrade, EnideCarrasco-Olivera, DanteManzaneda, Cristinainfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:17:51Zoai:ria.ua.pt:10773/39946Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:09:55.811698Repositório 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 On the Eigenvectors of Generalized Circulant Matrices
title On the Eigenvectors of Generalized Circulant Matrices
spellingShingle On the Eigenvectors of Generalized Circulant Matrices
Andrade, Enide
Circulant matrix
Permutation matrix
Generalized circulant matrix
Eigenvector
title_short On the Eigenvectors of Generalized Circulant Matrices
title_full On the Eigenvectors of Generalized Circulant Matrices
title_fullStr On the Eigenvectors of Generalized Circulant Matrices
title_full_unstemmed On the Eigenvectors of Generalized Circulant Matrices
title_sort On the Eigenvectors of Generalized Circulant Matrices
author Andrade, Enide
author_facet Andrade, Enide
Carrasco-Olivera, Dante
Manzaneda, Cristina
author_role author
author2 Carrasco-Olivera, Dante
Manzaneda, Cristina
author2_role author
author
dc.contributor.author.fl_str_mv Andrade, Enide
Carrasco-Olivera, Dante
Manzaneda, Cristina
dc.subject.por.fl_str_mv Circulant matrix
Permutation matrix
Generalized circulant matrix
Eigenvector
topic Circulant matrix
Permutation matrix
Generalized circulant matrix
Eigenvector
description In \cite{Mourad}, Kaddoura and Mourad, in order to widen the scope of the class of circulant matrices, (see \cite{Davis}), constructed circulant-like matrices that were called generalized weighted circulant matrices. These matrices form a class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. The characteristic polynomials, eigenvalues and eigenvectors of the generalized permutation matrices corresponding to a family of permutations were described. Additionally, the eigenvalues of the weighted circulant matrices were given. However, their eigenvectors were not studied. Having these results as motivation, we present, in some cases, explicit formulas for the eigenvectors of the generalized weighted circulant matrices. In this work, they are simply called generalized circulant matrices.
publishDate 2024
dc.date.none.fl_str_mv 2024-01-01T00:00:00Z
2024
2026-01-01T00:00:00Z
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/10773/39946
url http://hdl.handle.net/10773/39946
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0308-1087
10.1080/03081087.2023.2284750
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
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
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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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