Solving an open problem about the G-Drazin partial order

Autores
Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome, Néstor
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
G-Drazin inverses and the G-Drazin partial order for square matrices have been both recently introduced by Wang and Liu. They proved the following implication: If A is below B under the G-Drazin partial order, then any G-Drazin inverse of B is also a G-Drazin inverse of A. However, this necessary condition could not be stated as a characterization and the validity (or not) of the converse implication was posed as an open problem. In this paper, this problem is completely solved. It is obtained that the converse, in general, is false, and a form to construct counterexamples is provided. It is also proved that the converse holds under an additional condition (which is also necessary) as well as for some special cases of matrices.
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, Néstor. Universidad Politécnica de Valencia; España
Materia
G-DRAZIN INVERSE
G-DRAZIN PARTIAL ORDER
MINUS PARTIAL ORDER
SPACE PRE-ORDER
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/132022
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Solving an open problem about the G-Drazin partial orderFerreyra, David EduardoLattanzi, Marina BeatrizLevis, Fabián EduardoThome, NéstorG-DRAZIN INVERSEG-DRAZIN PARTIAL ORDERMINUS PARTIAL ORDERSPACE PRE-ORDERhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1G-Drazin inverses and the G-Drazin partial order for square matrices have been both recently introduced by Wang and Liu. They proved the following implication: If A is below B under the G-Drazin partial order, then any G-Drazin inverse of B is also a G-Drazin inverse of A. However, this necessary condition could not be stated as a characterization and the validity (or not) of the converse implication was posed as an open problem. In this paper, this problem is completely solved. It is obtained that the converse, in general, is false, and a form to construct counterexamples is provided. It is also proved that the converse holds under an additional condition (which is also necessary) as well as for some special cases of matrices.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, Néstor. Universidad Politécnica de Valencia; EspañaInternational Linear Algebra Society2020-02-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/132022Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome, Néstor; Solving an open problem about the G-Drazin partial order; International Linear Algebra Society; Electronic Journal Of Linear Algebra; 36; 1; 8-2-2020; 55-661081-3810CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.13001/ela.2020.4965info:eu-repo/semantics/altIdentifier/url/https://journals.uwyo.edu/index.php/ela/article/view/4965info:eu-repo/semantics/altIdentifier/url/https://riunet.upv.es/handle/10251/161871info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:22:29Zoai:ri.conicet.gov.ar:11336/132022instacron: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 14:22:30.111CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Solving an open problem about the G-Drazin partial order
title Solving an open problem about the G-Drazin partial order
spellingShingle Solving an open problem about the G-Drazin partial order
Ferreyra, David Eduardo
G-DRAZIN INVERSE
G-DRAZIN PARTIAL ORDER
MINUS PARTIAL ORDER
SPACE PRE-ORDER
title_short Solving an open problem about the G-Drazin partial order
title_full Solving an open problem about the G-Drazin partial order
title_fullStr Solving an open problem about the G-Drazin partial order
title_full_unstemmed Solving an open problem about the G-Drazin partial order
title_sort Solving an open problem about the G-Drazin partial order
dc.creator.none.fl_str_mv Ferreyra, David Eduardo
Lattanzi, Marina Beatriz
Levis, Fabián Eduardo
Thome, Néstor
author Ferreyra, David Eduardo
author_facet Ferreyra, David Eduardo
Lattanzi, Marina Beatriz
Levis, Fabián Eduardo
Thome, Néstor
author_role author
author2 Lattanzi, Marina Beatriz
Levis, Fabián Eduardo
Thome, Néstor
author2_role author
author
author
dc.subject.none.fl_str_mv G-DRAZIN INVERSE
G-DRAZIN PARTIAL ORDER
MINUS PARTIAL ORDER
SPACE PRE-ORDER
topic G-DRAZIN INVERSE
G-DRAZIN PARTIAL ORDER
MINUS PARTIAL ORDER
SPACE PRE-ORDER
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv G-Drazin inverses and the G-Drazin partial order for square matrices have been both recently introduced by Wang and Liu. They proved the following implication: If A is below B under the G-Drazin partial order, then any G-Drazin inverse of B is also a G-Drazin inverse of A. However, this necessary condition could not be stated as a characterization and the validity (or not) of the converse implication was posed as an open problem. In this paper, this problem is completely solved. It is obtained that the converse, in general, is false, and a form to construct counterexamples is provided. It is also proved that the converse holds under an additional condition (which is also necessary) as well as for some special cases of matrices.
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, Néstor. Universidad Politécnica de Valencia; España
description G-Drazin inverses and the G-Drazin partial order for square matrices have been both recently introduced by Wang and Liu. They proved the following implication: If A is below B under the G-Drazin partial order, then any G-Drazin inverse of B is also a G-Drazin inverse of A. However, this necessary condition could not be stated as a characterization and the validity (or not) of the converse implication was posed as an open problem. In this paper, this problem is completely solved. It is obtained that the converse, in general, is false, and a form to construct counterexamples is provided. It is also proved that the converse holds under an additional condition (which is also necessary) as well as for some special cases of matrices.
publishDate 2020
dc.date.none.fl_str_mv 2020-02-08
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/11336/132022
Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome, Néstor; Solving an open problem about the G-Drazin partial order; International Linear Algebra Society; Electronic Journal Of Linear Algebra; 36; 1; 8-2-2020; 55-66
1081-3810
CONICET Digital
CONICET
url http://hdl.handle.net/11336/132022
identifier_str_mv Ferreyra, David Eduardo; Lattanzi, Marina Beatriz; Levis, Fabián Eduardo; Thome, Néstor; Solving an open problem about the G-Drazin partial order; International Linear Algebra Society; Electronic Journal Of Linear Algebra; 36; 1; 8-2-2020; 55-66
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/doi/10.13001/ela.2020.4965
info:eu-repo/semantics/altIdentifier/url/https://journals.uwyo.edu/index.php/ela/article/view/4965
info:eu-repo/semantics/altIdentifier/url/https://riunet.upv.es/handle/10251/161871
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv 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
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score 13.22299

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