The group inverse of some circulant matrices

In a previous work the authors presented the necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three real parameters and, moreover, we obtained a closed formula for their inverse. The techniques we used allowed us to reduce the computational cost of...

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Autores: Carmona Mejías, Ángeles|||0000-0001-7713-1066, Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373, Jiménez Jiménez, María José|||0000-0003-3502-462X, Mitjana Riera, Margarida|||0000-0002-6563-5512
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/334026
Acceso en línea:https://hdl.handle.net/2117/334026
https://dx.doi.org/10.1016/j.laa.2020.11.002
Access Level:acceso abierto
Palabra clave:Algebras, Linear
Circulant matrix
Group Inverse
Difference Equations
Àlgebra lineal
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
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spelling The group inverse of some circulant matricesCarmona Mejías, Ángeles|||0000-0001-7713-1066Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373Jiménez Jiménez, María José|||0000-0003-3502-462XMitjana Riera, Margarida|||0000-0002-6563-5512Algebras, LinearCirculant matrixGroup InverseDifference EquationsÀlgebra linealClassificació AMS::15 Linear and multilinear algebramatrix theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilinealIn a previous work the authors presented the necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three real parameters and, moreover, we obtained a closed formula for their inverse. The techniques we used allowed us to reduce the computational cost of evaluating the inverse. In this work we complete the theoretical analysis of the mentioned circulant matrices by considering complex parameters and also the singular case. In addition, we explicitely compute the group inverse of a specific kind of this class of matrices using the same techniques that the authors developed for the non singular case; that is, solving first order linear difference equations.Elsevier20202020-11-1220202020-12-04journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/334026https://dx.doi.org/10.1016/j.laa.2020.11.002reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3340262026-05-27T15:37:01Z
dc.title.none.fl_str_mv The group inverse of some circulant matrices
title The group inverse of some circulant matrices
spellingShingle The group inverse of some circulant matrices
Carmona Mejías, Ángeles|||0000-0001-7713-1066
Algebras, Linear
Circulant matrix
Group Inverse
Difference Equations
Àlgebra lineal
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
title_short The group inverse of some circulant matrices
title_full The group inverse of some circulant matrices
title_fullStr The group inverse of some circulant matrices
title_full_unstemmed The group inverse of some circulant matrices
title_sort The group inverse of some circulant matrices
dc.creator.none.fl_str_mv Carmona Mejías, Ángeles|||0000-0001-7713-1066
Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Jiménez Jiménez, María José|||0000-0003-3502-462X
Mitjana Riera, Margarida|||0000-0002-6563-5512
author Carmona Mejías, Ángeles|||0000-0001-7713-1066
author_facet Carmona Mejías, Ángeles|||0000-0001-7713-1066
Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Jiménez Jiménez, María José|||0000-0003-3502-462X
Mitjana Riera, Margarida|||0000-0002-6563-5512
author_role author
author2 Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Jiménez Jiménez, María José|||0000-0003-3502-462X
Mitjana Riera, Margarida|||0000-0002-6563-5512
author2_role author
author
author
dc.subject.none.fl_str_mv Algebras, Linear
Circulant matrix
Group Inverse
Difference Equations
Àlgebra lineal
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
topic Algebras, Linear
Circulant matrix
Group Inverse
Difference Equations
Àlgebra lineal
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
description In a previous work the authors presented the necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three real parameters and, moreover, we obtained a closed formula for their inverse. The techniques we used allowed us to reduce the computational cost of evaluating the inverse. In this work we complete the theoretical analysis of the mentioned circulant matrices by considering complex parameters and also the singular case. In addition, we explicitely compute the group inverse of a specific kind of this class of matrices using the same techniques that the authors developed for the non singular case; that is, solving first order linear difference equations.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-11-12
2020
2020-12-04
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/334026
https://dx.doi.org/10.1016/j.laa.2020.11.002
url https://hdl.handle.net/2117/334026
https://dx.doi.org/10.1016/j.laa.2020.11.002
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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