Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k

Autores
Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome Coppo, Néstor Javier
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let A and E be n × n given complex matrices. This paper provides a necessary and sufficient condition for the solvability to the matrix equation system given by AXA = AEA and AkEAX = XAEAk, for k being the index of A. In addition, its general solution is derived in terms of a G-Drazin inverse of A. As consequences, new representations are obtained for the set of all G-Drazin inverses; some interesting applications are also derived to show the importance of the obtained formulas.
Fil: Ferreyra, David Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Lattanzi, Marina Beatriz. Universidad Nacional de la Pampa. Facultad de Cs.exactas y Naturales. Dto de Matemática; Argentina
Fil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Thome Coppo, Néstor Javier. Universidad Politécnica de Valencia; España
Materia
G-DRAZIN INVERSES
GENERALIZED INVERSES
INDEX
MATRIX EQUATIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/129825
Acceder
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spelling Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index kFerreyra, David EduardoLattanzi, Marina BeatrizLevis, Fabián EduardoThome Coppo, Néstor JavierG-DRAZIN INVERSESGENERALIZED INVERSESINDEXMATRIX EQUATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let A and E be n × n given complex matrices. This paper provides a necessary and sufficient condition for the solvability to the matrix equation system given by AXA = AEA and AkEAX = XAEAk, for k being the index of A. In addition, its general solution is derived in terms of a G-Drazin inverse of A. As consequences, new representations are obtained for the set of all G-Drazin inverses; some interesting applications are also derived to show the importance of the obtained formulas.Fil: Ferreyra, David Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Lattanzi, Marina Beatriz. Universidad Nacional de la Pampa. Facultad de Cs.exactas y Naturales. Dto de Matemática; ArgentinaFil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Thome Coppo, Néstor Javier. Universidad Politécnica de Valencia; EspañaInternational Linear Algebra Society2019-11-14info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/129825Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome Coppo, Néstor Javier; Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k; International Linear Algebra Society; Electronic Journal of Linear Algebra; 35; 1; 14-11-2019; 503-5101081-3810CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.uwyo.edu/index.php/ela/article/view/5169info:eu-repo/semantics/altIdentifier/doi/10.13001/1081-3810.4051info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:53:43Zoai:ri.conicet.gov.ar:11336/129825instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:53:44.02CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k
title Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k
spellingShingle Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k
Ferreyra, David Eduardo
G-DRAZIN INVERSES
GENERALIZED INVERSES
INDEX
MATRIX EQUATIONS
title_short Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k
title_full Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k
title_fullStr Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k
title_full_unstemmed Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k
title_sort Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k
dc.creator.none.fl_str_mv Ferreyra, David Eduardo
Lattanzi, Marina Beatriz
Levis, Fabián Eduardo
Thome Coppo, Néstor Javier
author Ferreyra, David Eduardo
author_facet Ferreyra, David Eduardo
Lattanzi, Marina Beatriz
Levis, Fabián Eduardo
Thome Coppo, Néstor Javier
author_role author
author2 Lattanzi, Marina Beatriz
Levis, Fabián Eduardo
Thome Coppo, Néstor Javier
author2_role author
author
author
dc.subject.none.fl_str_mv G-DRAZIN INVERSES
GENERALIZED INVERSES
INDEX
MATRIX EQUATIONS
topic G-DRAZIN INVERSES
GENERALIZED INVERSES
INDEX
MATRIX EQUATIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let A and E be n × n given complex matrices. This paper provides a necessary and sufficient condition for the solvability to the matrix equation system given by AXA = AEA and AkEAX = XAEAk, for k being the index of A. In addition, its general solution is derived in terms of a G-Drazin inverse of A. As consequences, new representations are obtained for the set of all G-Drazin inverses; some interesting applications are also derived to show the importance of the obtained formulas.
Fil: Ferreyra, David Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Lattanzi, Marina Beatriz. Universidad Nacional de la Pampa. Facultad de Cs.exactas y Naturales. Dto de Matemática; Argentina
Fil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Thome Coppo, Néstor Javier. Universidad Politécnica de Valencia; España
description Let A and E be n × n given complex matrices. This paper provides a necessary and sufficient condition for the solvability to the matrix equation system given by AXA = AEA and AkEAX = XAEAk, for k being the index of A. In addition, its general solution is derived in terms of a G-Drazin inverse of A. As consequences, new representations are obtained for the set of all G-Drazin inverses; some interesting applications are also derived to show the importance of the obtained formulas.
publishDate 2019
dc.date.none.fl_str_mv 2019-11-14
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/129825
Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome Coppo, Néstor Javier; Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k; International Linear Algebra Society; Electronic Journal of Linear Algebra; 35; 1; 14-11-2019; 503-510
1081-3810
CONICET Digital
CONICET
url http://hdl.handle.net/11336/129825
identifier_str_mv Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome Coppo, Néstor Javier; Parametrized solutions X of the system AXA=AEA and A^kEAX= XAEA^k for a matrix A having index k; International Linear Algebra Society; Electronic Journal of Linear Algebra; 35; 1; 14-11-2019; 503-510
1081-3810
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://journals.uwyo.edu/index.php/ela/article/view/5169
info:eu-repo/semantics/altIdentifier/doi/10.13001/1081-3810.4051
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv International Linear Algebra Society
publisher.none.fl_str_mv International Linear Algebra Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846083068618604544
score 13.22299

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