Characterizations of {K,s+1}-Potent Matrices and Applications

Recently, situations where a matrix coincides with some of its powers have been studied. This kind of matrices is related to the generalized inverse matrices. On the other hand, it is possible to introduce another class of matrices that involve an involutory matrix, generalizing the well-known idemp...

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Autores: Lebtahi Ep-Kadi-Hahifi, Leila, Romero Martínez, José Oscar|||0000-0003-4081-9005, Thome, Néstor|||0000-0001-5328-6637
Tipo de documento: artigo
Data de publicação:2012
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositório:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglês
OAI Identifier:oai:riunet.upv.es:10251/37709
Acesso em linha:https://riunet.upv.es/handle/10251/37709
Access Level:Acceso aberto
Palavra-chave:Group inverse matrix
Idempotent matrix
Involutory matrix
Spectrum
Block representation
Generalized inverse
Group inverse
Linear combinations
Matrix
Inverse problems
Matrix algebra
INGENIERIA TELEMATICA
MATEMATICA APLICADA
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repository_id_str
spelling Characterizations of {K,s+1}-Potent Matrices and ApplicationsLebtahi Ep-Kadi-Hahifi, LeilaRomero Martínez, José Oscar|||0000-0003-4081-9005Thome, Néstor|||0000-0001-5328-6637Group inverse matrixIdempotent matrixInvolutory matrixSpectrumBlock representationGeneralized inverseGroup inverseLinear combinationsMatrixInverse problemsMatrix algebraINGENIERIA TELEMATICAMATEMATICA APLICADARecently, situations where a matrix coincides with some of its powers have been studied. This kind of matrices is related to the generalized inverse matrices. On the other hand, it is possible to introduce another class of matrices that involve an involutory matrix, generalizing the well-known idempotent matrix, widely useful in many applications. In this paper, we introduce a new kind of matrices called {K,s+1}-potent, as an extension of the aforementioned ones. First, different properties of {K,s+1}-potent matrices have been developed. Later, the main result developed in this paper is the characterization of this kind of matrices from a spectral point of view, in terms of powers of the matrix, by means of the group inverse and, via a block representation of a matrix of index 1. Finally, an application of the above results to study linear combinations of {K,s+1}-potent matrices is derived. © 2010 Elsevier Inc. All rights reserved.ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaDepartamento de ComunicacionesInstituto Universitario de Matemática MultidisciplinarInstituto de Investigación para la Gestión Integrada de Zonas CosterasRepositorio Institucional de la Universitat Politècnica de València Riunet20122012-01-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/37709reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/377092026-06-13T07:49:27Z
dc.title.none.fl_str_mv Characterizations of {K,s+1}-Potent Matrices and Applications
title Characterizations of {K,s+1}-Potent Matrices and Applications
spellingShingle Characterizations of {K,s+1}-Potent Matrices and Applications
Lebtahi Ep-Kadi-Hahifi, Leila
Group inverse matrix
Idempotent matrix
Involutory matrix
Spectrum
Block representation
Generalized inverse
Group inverse
Linear combinations
Matrix
Inverse problems
Matrix algebra
INGENIERIA TELEMATICA
MATEMATICA APLICADA
title_short Characterizations of {K,s+1}-Potent Matrices and Applications
title_full Characterizations of {K,s+1}-Potent Matrices and Applications
title_fullStr Characterizations of {K,s+1}-Potent Matrices and Applications
title_full_unstemmed Characterizations of {K,s+1}-Potent Matrices and Applications
title_sort Characterizations of {K,s+1}-Potent Matrices and Applications
dc.creator.none.fl_str_mv Lebtahi Ep-Kadi-Hahifi, Leila
Romero Martínez, José Oscar|||0000-0003-4081-9005
Thome, Néstor|||0000-0001-5328-6637
author Lebtahi Ep-Kadi-Hahifi, Leila
author_facet Lebtahi Ep-Kadi-Hahifi, Leila
Romero Martínez, José Oscar|||0000-0003-4081-9005
Thome, Néstor|||0000-0001-5328-6637
author_role author
author2 Romero Martínez, José Oscar|||0000-0003-4081-9005
Thome, Néstor|||0000-0001-5328-6637
author2_role author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Departamento de Comunicaciones
Instituto Universitario de Matemática Multidisciplinar
Instituto de Investigación para la Gestión Integrada de Zonas Costeras
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Group inverse matrix
Idempotent matrix
Involutory matrix
Spectrum
Block representation
Generalized inverse
Group inverse
Linear combinations
Matrix
Inverse problems
Matrix algebra
INGENIERIA TELEMATICA
MATEMATICA APLICADA
topic Group inverse matrix
Idempotent matrix
Involutory matrix
Spectrum
Block representation
Generalized inverse
Group inverse
Linear combinations
Matrix
Inverse problems
Matrix algebra
INGENIERIA TELEMATICA
MATEMATICA APLICADA
description Recently, situations where a matrix coincides with some of its powers have been studied. This kind of matrices is related to the generalized inverse matrices. On the other hand, it is possible to introduce another class of matrices that involve an involutory matrix, generalizing the well-known idempotent matrix, widely useful in many applications. In this paper, we introduce a new kind of matrices called {K,s+1}-potent, as an extension of the aforementioned ones. First, different properties of {K,s+1}-potent matrices have been developed. Later, the main result developed in this paper is the characterization of this kind of matrices from a spectral point of view, in terms of powers of the matrix, by means of the group inverse and, via a block representation of a matrix of index 1. Finally, an application of the above results to study linear combinations of {K,s+1}-potent matrices is derived. © 2010 Elsevier Inc. All rights reserved.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/37709
url https://riunet.upv.es/handle/10251/37709
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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