On the C-determinantal range for special classes of matrices

Detalhes bibliográficos
Autor(a) principal: Guterman, Alexander
Data de Publicação: 2016
Outros Autores: Lemos, Rute, Soares, Graça
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/15348
Resumo: Let A and C be square complex matrices of sizen, the C-determinantal range of A is the subset of the complex plane{det(A−UCU^∗): UU^∗=In}. If A, C are both Hermitian matrices, then by a result of Fiedler (1971)[11] this set is a real line segment. In our paper we study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two well-known results on this topic. The first result is due to Li concerning theC-numerical range of a Hermitian matrix, see Condition 5.1 (a) in Li, (1994)[20]. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et al. (2008)[21], Theorem 3.3).
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spelling On the C-determinantal range for special classes of matricesC-determinantal rangeC-numerical rangeMarcus-Oliveira conjectureσ-pointsReal setsLet A and C be square complex matrices of sizen, the C-determinantal range of A is the subset of the complex plane{det(A−UCU^∗): UU^∗=In}. If A, C are both Hermitian matrices, then by a result of Fiedler (1971)[11] this set is a real line segment. In our paper we study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two well-known results on this topic. The first result is due to Li concerning theC-numerical range of a Hermitian matrix, see Condition 5.1 (a) in Li, (1994)[20]. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et al. (2008)[21], Theorem 3.3).Elsevier2017-02-15T00:00:00Z2016-02-15T00:00:00Z2016-02-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15348eng0096-300310.1016/j.amc.2015.11.042Guterman, AlexanderLemos, RuteSoares, Graçainfo: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:RCAAP2024-02-22T11:28:09Zoai:ria.ua.pt:10773/15348Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:39.054530Repositório 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 On the C-determinantal range for special classes of matrices
title On the C-determinantal range for special classes of matrices
spellingShingle On the C-determinantal range for special classes of matrices
Guterman, Alexander
C-determinantal range
C-numerical range
Marcus-Oliveira conjecture
σ-points
Real sets
title_short On the C-determinantal range for special classes of matrices
title_full On the C-determinantal range for special classes of matrices
title_fullStr On the C-determinantal range for special classes of matrices
title_full_unstemmed On the C-determinantal range for special classes of matrices
title_sort On the C-determinantal range for special classes of matrices
author Guterman, Alexander
author_facet Guterman, Alexander
Lemos, Rute
Soares, Graça
author_role author
author2 Lemos, Rute
Soares, Graça
author2_role author
author
dc.contributor.author.fl_str_mv Guterman, Alexander
Lemos, Rute
Soares, Graça
dc.subject.por.fl_str_mv C-determinantal range
C-numerical range
Marcus-Oliveira conjecture
σ-points
Real sets
topic C-determinantal range
C-numerical range
Marcus-Oliveira conjecture
σ-points
Real sets
description Let A and C be square complex matrices of sizen, the C-determinantal range of A is the subset of the complex plane{det(A−UCU^∗): UU^∗=In}. If A, C are both Hermitian matrices, then by a result of Fiedler (1971)[11] this set is a real line segment. In our paper we study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two well-known results on this topic. The first result is due to Li concerning theC-numerical range of a Hermitian matrix, see Condition 5.1 (a) in Li, (1994)[20]. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et al. (2008)[21], Theorem 3.3).
publishDate 2016
dc.date.none.fl_str_mv 2016-02-15T00:00:00Z
2016-02-15
2017-02-15T00:00:00Z
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/10773/15348
url http://hdl.handle.net/10773/15348
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0096-3003
10.1016/j.amc.2015.11.042
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
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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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