Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case

Detalhes bibliográficos
Autor(a) principal: Johnson, Charles R.
Data de Publicação: 2012
Outros Autores: Lewis, Drew, Zhang Yulin
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/20760
Resumo: For the problem of which Jordan forms are possible for n × n complex matrices A, B and C, when A = BC, geometric multiplicity restrictions are given for the eigenvalues of the three matrices. Together with the obvious determinantal condition on the eigenvalues, these necessary conditions are shown to be sufficient for the problem when n < 4, but not for n ≥ 4. Some basic observations about the problem are given in the process.
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spelling Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 caseJordan formGeometric multiplicityMatrix productScience & TechnologyFor the problem of which Jordan forms are possible for n × n complex matrices A, B and C, when A = BC, geometric multiplicity restrictions are given for the eigenvalues of the three matrices. Together with the obvious determinantal condition on the eigenvalues, these necessary conditions are shown to be sufficient for the problem when n < 4, but not for n ≥ 4. Some basic observations about the problem are given in the process.National Science Foundation, USA and FCT, Portugal.World Scientific Publishing CompanyUniversidade do MinhoJohnson, Charles R.Lewis, DrewZhang Yulin20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/20760eng1793-557110.1142/S1793557112500362www.worldscientific.cominfo: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:RCAAP2023-07-21T12:48:18Zoai:repositorium.sdum.uminho.pt:1822/20760Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:46:29.697671Repositório 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 Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case
title Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case
spellingShingle Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case
Johnson, Charles R.
Jordan form
Geometric multiplicity
Matrix product
Science & Technology
title_short Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case
title_full Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case
title_fullStr Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case
title_full_unstemmed Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case
title_sort Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case
author Johnson, Charles R.
author_facet Johnson, Charles R.
Lewis, Drew
Zhang Yulin
author_role author
author2 Lewis, Drew
Zhang Yulin
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Johnson, Charles R.
Lewis, Drew
Zhang Yulin
dc.subject.por.fl_str_mv Jordan form
Geometric multiplicity
Matrix product
Science & Technology
topic Jordan form
Geometric multiplicity
Matrix product
Science & Technology
description For the problem of which Jordan forms are possible for n × n complex matrices A, B and C, when A = BC, geometric multiplicity restrictions are given for the eigenvalues of the three matrices. Together with the obvious determinantal condition on the eigenvalues, these necessary conditions are shown to be sufficient for the problem when n < 4, but not for n ≥ 4. Some basic observations about the problem are given in the process.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01T00:00:00Z
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/1822/20760
url http://hdl.handle.net/1822/20760
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1793-5571
10.1142/S1793557112500362
www.worldscientific.com
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 World Scientific Publishing Company
publisher.none.fl_str_mv World Scientific Publishing Company
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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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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