Weak matrix majorization

Autores
Martínez Pería, Francisco Dardo; Massey, Pedro Gustavo; Silvestre, Luis E.
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given X,Y∈Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization,X≻wYifthereexistsarow- stochasticmatrixA∈Rn×nsuchthatAX=Y,and consider the relations between this concept, strong majorization (≻s) and directional majorization (≻). It is verified that ≻s ⇒ ≻ ⇒ ≻w, but none of the reciprocal implications is true. Nevertheless, we study the implications ≻w ⇒ ≻s and ≻ ⇒ ≻s under additional hypotheses. We give characterizations of strong, directional and weak matrix majorization in terms of convexity. We also introduce definitions for majorization between Abelian families of selfadjoint matrices, called joint majorizations. They are induced by the previously mentioned matrix majorizations. We obtain descriptions of these relations using convexity arguments.
Facultad de Ciencias Exactas
Materia
Matemática
Convex sets and functions
Multivariate and directional matrix majorizations
Mutually commuting selfadjoint matrices
Row stochastic matrices
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/83248
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/83248
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Weak matrix majorizationMartínez Pería, Francisco DardoMassey, Pedro GustavoSilvestre, Luis E.MatemáticaConvex sets and functionsMultivariate and directional matrix majorizationsMutually commuting selfadjoint matricesRow stochastic matricesGiven X,Y∈Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization,X≻wYifthereexistsarow- stochasticmatrixA∈Rn×nsuchthatAX=Y,and consider the relations between this concept, strong majorization (≻s) and directional majorization (≻). It is verified that ≻s ⇒ ≻ ⇒ ≻w, but none of the reciprocal implications is true. Nevertheless, we study the implications ≻w ⇒ ≻s and ≻ ⇒ ≻s under additional hypotheses. We give characterizations of strong, directional and weak matrix majorization in terms of convexity. We also introduce definitions for majorization between Abelian families of selfadjoint matrices, called joint majorizations. They are induced by the previously mentioned matrix majorizations. We obtain descriptions of these relations using convexity arguments.Facultad de Ciencias Exactas2005info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf343-368http://sedici.unlp.edu.ar/handle/10915/83248enginfo:eu-repo/semantics/altIdentifier/issn/0024-3795info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2005.02.003info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:07:42Zoai:sedici.unlp.edu.ar:10915/83248Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:07:42.641SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Weak matrix majorization
title Weak matrix majorization
spellingShingle Weak matrix majorization
Martínez Pería, Francisco Dardo
Matemática
Convex sets and functions
Multivariate and directional matrix majorizations
Mutually commuting selfadjoint matrices
Row stochastic matrices
title_short Weak matrix majorization
title_full Weak matrix majorization
title_fullStr Weak matrix majorization
title_full_unstemmed Weak matrix majorization
title_sort Weak matrix majorization
dc.creator.none.fl_str_mv Martínez Pería, Francisco Dardo
Massey, Pedro Gustavo
Silvestre, Luis E.
author Martínez Pería, Francisco Dardo
author_facet Martínez Pería, Francisco Dardo
Massey, Pedro Gustavo
Silvestre, Luis E.
author_role author
author2 Massey, Pedro Gustavo
Silvestre, Luis E.
author2_role author
author
dc.subject.none.fl_str_mv Matemática
Convex sets and functions
Multivariate and directional matrix majorizations
Mutually commuting selfadjoint matrices
Row stochastic matrices
topic Matemática
Convex sets and functions
Multivariate and directional matrix majorizations
Mutually commuting selfadjoint matrices
Row stochastic matrices
dc.description.none.fl_txt_mv Given X,Y∈Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization,X≻wYifthereexistsarow- stochasticmatrixA∈Rn×nsuchthatAX=Y,and consider the relations between this concept, strong majorization (≻s) and directional majorization (≻). It is verified that ≻s ⇒ ≻ ⇒ ≻w, but none of the reciprocal implications is true. Nevertheless, we study the implications ≻w ⇒ ≻s and ≻ ⇒ ≻s under additional hypotheses. We give characterizations of strong, directional and weak matrix majorization in terms of convexity. We also introduce definitions for majorization between Abelian families of selfadjoint matrices, called joint majorizations. They are induced by the previously mentioned matrix majorizations. We obtain descriptions of these relations using convexity arguments.
Facultad de Ciencias Exactas
description Given X,Y∈Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization,X≻wYifthereexistsarow- stochasticmatrixA∈Rn×nsuchthatAX=Y,and consider the relations between this concept, strong majorization (≻s) and directional majorization (≻). It is verified that ≻s ⇒ ≻ ⇒ ≻w, but none of the reciprocal implications is true. Nevertheless, we study the implications ≻w ⇒ ≻s and ≻ ⇒ ≻s under additional hypotheses. We give characterizations of strong, directional and weak matrix majorization in terms of convexity. We also introduce definitions for majorization between Abelian families of selfadjoint matrices, called joint majorizations. They are induced by the previously mentioned matrix majorizations. We obtain descriptions of these relations using convexity arguments.
publishDate 2005
dc.date.none.fl_str_mv 2005
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/83248
url http://sedici.unlp.edu.ar/handle/10915/83248
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0024-3795
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2005.02.003
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
343-368
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 13.22299

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