Weak matrix majorization

Autores
Martinez Peria, Francisco Dardo; Massey, Pedro Gustavo; Silvestre, Luis Enrique
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≻ w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = 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.
Fil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Silvestre, Luis Enrique. University of Texas at Austin; Estados Unidos
Materia
MULTIVARIATE AND DIRECTIONAL MATRIX MAJORIZATIONS
ROW STOCHASTIC MATRICES
MUTUALLY COMMUTING SELFADJOINT MATRICES
CONVEX SETS AND FUNCTIONS
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:11336/108527
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/108527
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Weak matrix majorizationMartinez Peria, Francisco DardoMassey, Pedro GustavoSilvestre, Luis EnriqueMULTIVARIATE AND DIRECTIONAL MATRIX MAJORIZATIONSROW STOCHASTIC MATRICESMUTUALLY COMMUTING SELFADJOINT MATRICESCONVEX SETS AND FUNCTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given X, Y ∈ Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization, X≻ w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = 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.Fil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Silvestre, Luis Enrique. University of Texas at Austin; Estados UnidosElsevier Science Inc2005-07info: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/11336/108527Martinez Peria, Francisco Dardo; Massey, Pedro Gustavo; Silvestre, Luis Enrique; Weak matrix majorization; Elsevier Science Inc; Linear Algebra and its Applications; 403; 7-2005; 343-3680024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379505000741info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2005.02.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:44:51Zoai:ri.conicet.gov.ar:11336/108527instacron: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 14:44:51.769CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weak matrix majorization
title Weak matrix majorization
spellingShingle Weak matrix majorization
Martinez Peria, Francisco Dardo
MULTIVARIATE AND DIRECTIONAL MATRIX MAJORIZATIONS
ROW STOCHASTIC MATRICES
MUTUALLY COMMUTING SELFADJOINT MATRICES
CONVEX SETS AND FUNCTIONS
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 Martinez Peria, Francisco Dardo
Massey, Pedro Gustavo
Silvestre, Luis Enrique
author Martinez Peria, Francisco Dardo
author_facet Martinez Peria, Francisco Dardo
Massey, Pedro Gustavo
Silvestre, Luis Enrique
author_role author
author2 Massey, Pedro Gustavo
Silvestre, Luis Enrique
author2_role author
author
dc.subject.none.fl_str_mv MULTIVARIATE AND DIRECTIONAL MATRIX MAJORIZATIONS
ROW STOCHASTIC MATRICES
MUTUALLY COMMUTING SELFADJOINT MATRICES
CONVEX SETS AND FUNCTIONS
topic MULTIVARIATE AND DIRECTIONAL MATRIX MAJORIZATIONS
ROW STOCHASTIC MATRICES
MUTUALLY COMMUTING SELFADJOINT MATRICES
CONVEX SETS AND FUNCTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given X, Y ∈ Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization, X≻ w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = 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.
Fil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Silvestre, Luis Enrique. University of Texas at Austin; Estados Unidos
description Given X, Y ∈ Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization, X≻ w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = 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 2005-07
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/11336/108527
Martinez Peria, Francisco Dardo; Massey, Pedro Gustavo; Silvestre, Luis Enrique; Weak matrix majorization; Elsevier Science Inc; Linear Algebra and its Applications; 403; 7-2005; 343-368
0024-3795
CONICET Digital
CONICET
url http://hdl.handle.net/11336/108527
identifier_str_mv Martinez Peria, Francisco Dardo; Massey, Pedro Gustavo; Silvestre, Luis Enrique; Weak matrix majorization; Elsevier Science Inc; Linear Algebra and its Applications; 403; 7-2005; 343-368
0024-3795
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://www.sciencedirect.com/science/article/pii/S0024379505000741
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2005.02.003
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 Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
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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