The jordan form problem for C=AB : the balanced, diagonalizable case

Detalhes bibliográficos
Autor(a) principal: Johnson, Charles R.
Data de Publicação: 2010
Outros Autores: 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/1822/11449
Resumo: We consider a key case in the fundamental and substantial prob- lem of the possible Jordan canonical forms of A;B;C \in Mn(F) when C = AB. If A \in M2k(F) (respectively B;C \in M2k(F) ) is diagonalizable with two distinct eigenvalues a1; a2 (respectively b1; b2, and c1; c2), each with multiplicity k, and when C = AB, all possibilities for a1; a2; b1; b2; c1; c2 are characterized. The possibilities are much more restrictive than the ob- vious determinant condition: (a1a2b1b2)k = (c1c2)k allows. This is then used to settle the general, two eigenvalue per matrix, diagonalizable case of the Jordan form problem for C = AB.
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spelling The jordan form problem for C=AB : the balanced, diagonalizable caseJordan formMatrix productRankNull spacenull space, rankScience & TechnologyWe consider a key case in the fundamental and substantial prob- lem of the possible Jordan canonical forms of A;B;C \in Mn(F) when C = AB. If A \in M2k(F) (respectively B;C \in M2k(F) ) is diagonalizable with two distinct eigenvalues a1; a2 (respectively b1; b2, and c1; c2), each with multiplicity k, and when C = AB, all possibilities for a1; a2; b1; b2; c1; c2 are characterized. The possibilities are much more restrictive than the ob- vious determinant condition: (a1a2b1b2)k = (c1c2)k allows. This is then used to settle the general, two eigenvalue per matrix, diagonalizable case of the Jordan form problem for C = AB.Fundação para a Ciência e a Tecnologia (FCT)World Scientific and Engineering Academy and Society (WSEAS)Universidade do MinhoJohnson, Charles R.Zhang Yulin20102010-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/11449eng"Asian-European Journal of Mathematics". ISSN 1793-5571. 3:4 (2010) 609-623.1793-557110.1142/S1793557110000477info: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:RCAAP2023-07-21T12:22:29Zoai:repositorium.sdum.uminho.pt:1822/11449Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:15:59.293465Repositório 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 The jordan form problem for C=AB : the balanced, diagonalizable case
title The jordan form problem for C=AB : the balanced, diagonalizable case
spellingShingle The jordan form problem for C=AB : the balanced, diagonalizable case
Johnson, Charles R.
Jordan form
Matrix product
Rank
Null space
null space, rank
Science & Technology
title_short The jordan form problem for C=AB : the balanced, diagonalizable case
title_full The jordan form problem for C=AB : the balanced, diagonalizable case
title_fullStr The jordan form problem for C=AB : the balanced, diagonalizable case
title_full_unstemmed The jordan form problem for C=AB : the balanced, diagonalizable case
title_sort The jordan form problem for C=AB : the balanced, diagonalizable case
author Johnson, Charles R.
author_facet Johnson, Charles R.
Zhang Yulin
author_role author
author2 Zhang Yulin
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Johnson, Charles R.
Zhang Yulin
dc.subject.por.fl_str_mv Jordan form
Matrix product
Rank
Null space
null space, rank
Science & Technology
topic Jordan form
Matrix product
Rank
Null space
null space, rank
Science & Technology
description We consider a key case in the fundamental and substantial prob- lem of the possible Jordan canonical forms of A;B;C \in Mn(F) when C = AB. If A \in M2k(F) (respectively B;C \in M2k(F) ) is diagonalizable with two distinct eigenvalues a1; a2 (respectively b1; b2, and c1; c2), each with multiplicity k, and when C = AB, all possibilities for a1; a2; b1; b2; c1; c2 are characterized. The possibilities are much more restrictive than the ob- vious determinant condition: (a1a2b1b2)k = (c1c2)k allows. This is then used to settle the general, two eigenvalue per matrix, diagonalizable case of the Jordan form problem for C = AB.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-01-01T00:00:00Z
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/1822/11449
url http://hdl.handle.net/1822/11449
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Asian-European Journal of Mathematics". ISSN 1793-5571. 3:4 (2010) 609-623.
1793-5571
10.1142/S1793557110000477
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 and Engineering Academy and Society (WSEAS)
publisher.none.fl_str_mv World Scientific and Engineering Academy and Society (WSEAS)
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
repository.mail.fl_str_mv
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