Weak matrix majorization

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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 ⇒ ≻ ⇒...

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Autores principales: Martínez Pería, Francisco Dardo, Massey, Pedro Gustavo, Silvestre, Luis E.
Formato: Articulo
Lenguaje:Inglés
Publicado: 2005
Materias:
Matemática
Convex sets and functions
Multivariate and directional matrix majorizations
Mutually commuting selfadjoint matrices
Row stochastic matrices
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/83248
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-83248
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Convex sets and functions
Multivariate and directional matrix majorizations
Mutually commuting selfadjoint matrices
Row stochastic matrices
spellingShingle Matemática
Convex sets and functions
Multivariate and directional matrix majorizations
Mutually commuting selfadjoint matrices
Row stochastic matrices
Martínez Pería, Francisco Dardo
Massey, Pedro Gustavo
Silvestre, Luis E.
Weak matrix majorization
topic_facet Matemática
Convex sets and functions
Multivariate and directional matrix majorizations
Mutually commuting selfadjoint matrices
Row stochastic matrices
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.
format Articulo
Articulo
author Martínez Pería, Francisco Dardo
Massey, Pedro Gustavo
Silvestre, Luis E.
author_facet Martínez Pería, Francisco Dardo
Massey, Pedro Gustavo
Silvestre, Luis E.
author_sort Martínez Pería, Francisco Dardo
title Weak matrix majorization
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
publishDate 2005
url http://sedici.unlp.edu.ar/handle/10915/83248
work_keys_str_mv AT martinezperiafranciscodardo weakmatrixmajorization
AT masseypedrogustavo weakmatrixmajorization
AT silvestreluise weakmatrixmajorization
bdutipo_str Repositorios
_version_ 1764820488427667457

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