Some log-majorizations and an extension of a determinantal inequality

Detalhes bibliográficos
Autor(a) principal: Lemos, R.
Data de Publicação: 2018
Outros Autores: Soares, G.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/22956
Resumo: An eigenvalue inequality involving a matrix connection and its dual is established, and some log-majorization type results are obtained. In particular, some eigenvalues inequalities considered by F. Hiai and M. Lin [9], an associated conjecture, and a singular values inequality by L. Zou [20] are revisited. A reformulation of the inequality det(A+U^⁎B)≤det(A+B), for positive semidefinite matrices A,B, with U a unitary matrix that appears in the polar decomposition of B A, is also extended, using some known norm inequalities, associated to Furuta inequality and Araki–Cordes inequality.
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spelling Some log-majorizations and an extension of a determinantal inequalityAraki–Cordes inequalityEigenvaluesFuruta inequalityLog majorizationLöwner–Heinz inequalityMatrix connections and meansSingular valuesTrace and determinantal inequalitiesAn eigenvalue inequality involving a matrix connection and its dual is established, and some log-majorization type results are obtained. In particular, some eigenvalues inequalities considered by F. Hiai and M. Lin [9], an associated conjecture, and a singular values inequality by L. Zou [20] are revisited. A reformulation of the inequality det(A+U^⁎B)≤det(A+B), for positive semidefinite matrices A,B, with U a unitary matrix that appears in the polar decomposition of B A, is also extended, using some known norm inequalities, associated to Furuta inequality and Araki–Cordes inequality.Elsevier2018-04-23T15:29:44Z2018-01-01T00:00:00Z2018info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/22956eng0024-379510.1016/j.laa.2018.02.015Lemos, R.Soares, G.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:44:37Zoai:ria.ua.pt:10773/22956Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:56:50.258828Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Some log-majorizations and an extension of a determinantal inequality
title Some log-majorizations and an extension of a determinantal inequality
spellingShingle Some log-majorizations and an extension of a determinantal inequality
Lemos, R.
Araki–Cordes inequality
Eigenvalues
Furuta inequality
Log majorization
Löwner–Heinz inequality
Matrix connections and means
Singular values
Trace and determinantal inequalities
title_short Some log-majorizations and an extension of a determinantal inequality
title_full Some log-majorizations and an extension of a determinantal inequality
title_fullStr Some log-majorizations and an extension of a determinantal inequality
title_full_unstemmed Some log-majorizations and an extension of a determinantal inequality
title_sort Some log-majorizations and an extension of a determinantal inequality
author Lemos, R.
author_facet Lemos, R.
Soares, G.
author_role author
author2 Soares, G.
author2_role author
dc.contributor.author.fl_str_mv Lemos, R.
Soares, G.
dc.subject.por.fl_str_mv Araki–Cordes inequality
Eigenvalues
Furuta inequality
Log majorization
Löwner–Heinz inequality
Matrix connections and means
Singular values
Trace and determinantal inequalities
topic Araki–Cordes inequality
Eigenvalues
Furuta inequality
Log majorization
Löwner–Heinz inequality
Matrix connections and means
Singular values
Trace and determinantal inequalities
description An eigenvalue inequality involving a matrix connection and its dual is established, and some log-majorization type results are obtained. In particular, some eigenvalues inequalities considered by F. Hiai and M. Lin [9], an associated conjecture, and a singular values inequality by L. Zou [20] are revisited. A reformulation of the inequality det(A+U^⁎B)≤det(A+B), for positive semidefinite matrices A,B, with U a unitary matrix that appears in the polar decomposition of B A, is also extended, using some known norm inequalities, associated to Furuta inequality and Araki–Cordes inequality.
publishDate 2018
dc.date.none.fl_str_mv 2018-04-23T15:29:44Z
2018-01-01T00:00:00Z
2018
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/22956
url http://hdl.handle.net/10773/22956
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0024-3795
10.1016/j.laa.2018.02.015
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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