Quaternionic numerical range of complex matrices

Detalhes bibliográficos
Autor(a) principal: Carvalho, L.
Data de Publicação: 2021
Outros Autores: Diogo, C., Mendes, S.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10071/22382
Resumo: This paper explores further the computation of the quaternionic numerical range of a complex matrix. We prove a modified version of a conjecture by So and Thompson. Specifically, we show that the shape of the quaternionic numerical range for a complex matrix depends on the complex numerical range and two real values. We establish under which conditions the bild of a complex matrix coincides with its complex numerical range and when the quaternionic numerical range is convex.
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spelling Quaternionic numerical range of complex matricesQuaternionsNumerical rangeComplex matricesNumerical radiusThis paper explores further the computation of the quaternionic numerical range of a complex matrix. We prove a modified version of a conjecture by So and Thompson. Specifically, we show that the shape of the quaternionic numerical range for a complex matrix depends on the complex numerical range and two real values. We establish under which conditions the bild of a complex matrix coincides with its complex numerical range and when the quaternionic numerical range is convex.Elsevier2023-03-04T00:00:00Z2021-01-01T00:00:00Z20212021-03-19T20:00:27Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/22382eng0024-379510.1016/j.laa.2021.02.030Carvalho, L.Diogo, C.Mendes, S.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:RCAAP2023-11-09T17:54:56Zoai:repositorio.iscte-iul.pt:10071/22382Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:27:51.925857Repositório 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 Quaternionic numerical range of complex matrices
title Quaternionic numerical range of complex matrices
spellingShingle Quaternionic numerical range of complex matrices
Carvalho, L.
Quaternions
Numerical range
Complex matrices
Numerical radius
title_short Quaternionic numerical range of complex matrices
title_full Quaternionic numerical range of complex matrices
title_fullStr Quaternionic numerical range of complex matrices
title_full_unstemmed Quaternionic numerical range of complex matrices
title_sort Quaternionic numerical range of complex matrices
author Carvalho, L.
author_facet Carvalho, L.
Diogo, C.
Mendes, S.
author_role author
author2 Diogo, C.
Mendes, S.
author2_role author
author
dc.contributor.author.fl_str_mv Carvalho, L.
Diogo, C.
Mendes, S.
dc.subject.por.fl_str_mv Quaternions
Numerical range
Complex matrices
Numerical radius
topic Quaternions
Numerical range
Complex matrices
Numerical radius
description This paper explores further the computation of the quaternionic numerical range of a complex matrix. We prove a modified version of a conjecture by So and Thompson. Specifically, we show that the shape of the quaternionic numerical range for a complex matrix depends on the complex numerical range and two real values. We establish under which conditions the bild of a complex matrix coincides with its complex numerical range and when the quaternionic numerical range is convex.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01T00:00:00Z
2021
2021-03-19T20:00:27Z
2023-03-04T00:00:00Z
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/10071/22382
url http://hdl.handle.net/10071/22382
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0024-3795
10.1016/j.laa.2021.02.030
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)
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
repository.mail.fl_str_mv
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