Further geometric restrictions on jordan structure in matrix factorization
Main Author: | |
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Publication Date: | 2012 |
Other Authors: | , |
Format: | Article |
Language: | eng |
Source: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Download full: | http://hdl.handle.net/1822/20485 |
Summary: | It is known that a nonsingular, nonscalar, n-by-n complex matrix A may be factored as A = BC, in which the spectra of B and C are arbitrary, subject to det(A) = det(B)det(C). It has been shown that when two matrices have eigenvalues of high geometric multiplicity, this restricts the possible Jordan structure of the third. We demonstrate a previously unknown restriction on the Jordan structures of B and C. Furthermore, we show that this generalized geometric multiplicity restriction implies the already known geometric multiplicity restriction, show that the new more restrictive condition is not sufficient in general but is sufficient in a situation that we identify. |
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Further geometric restrictions on jordan structure in matrix factorizationJordan formMatrix product.Geometric multiplicityScience & TechnologyIt is known that a nonsingular, nonscalar, n-by-n complex matrix A may be factored as A = BC, in which the spectra of B and C are arbitrary, subject to det(A) = det(B)det(C). It has been shown that when two matrices have eigenvalues of high geometric multiplicity, this restricts the possible Jordan structure of the third. We demonstrate a previously unknown restriction on the Jordan structures of B and C. Furthermore, we show that this generalized geometric multiplicity restriction implies the already known geometric multiplicity restriction, show that the new more restrictive condition is not sufficient in general but is sufficient in a situation that we identify.Fundação para a Ciência e a Tecnologia (FCT), National Science Foundation Grant DMS-03-53510, USAWorld Scientific Publishing CompanyUniversidade do MinhoJohnson, Charles R.Lewis, DrewZhang Yulin2012-062012-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/20485eng1793-557110.1142/S1793557112500180www.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:RCAAP2023-07-21T12:14:43Zoai:repositorium.sdum.uminho.pt:1822/20485Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:07:03.293992Repositório 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 |
Further geometric restrictions on jordan structure in matrix factorization |
title |
Further geometric restrictions on jordan structure in matrix factorization |
spellingShingle |
Further geometric restrictions on jordan structure in matrix factorization Johnson, Charles R. Jordan form Matrix product. Geometric multiplicity Science & Technology |
title_short |
Further geometric restrictions on jordan structure in matrix factorization |
title_full |
Further geometric restrictions on jordan structure in matrix factorization |
title_fullStr |
Further geometric restrictions on jordan structure in matrix factorization |
title_full_unstemmed |
Further geometric restrictions on jordan structure in matrix factorization |
title_sort |
Further geometric restrictions on jordan structure in matrix factorization |
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 Matrix product. Geometric multiplicity Science & Technology |
topic |
Jordan form Matrix product. Geometric multiplicity Science & Technology |
description |
It is known that a nonsingular, nonscalar, n-by-n complex matrix A may be factored as A = BC, in which the spectra of B and C are arbitrary, subject to det(A) = det(B)det(C). It has been shown that when two matrices have eigenvalues of high geometric multiplicity, this restricts the possible Jordan structure of the third. We demonstrate a previously unknown restriction on the Jordan structures of B and C. Furthermore, we show that this generalized geometric multiplicity restriction implies the already known geometric multiplicity restriction, show that the new more restrictive condition is not sufficient in general but is sufficient in a situation that we identify. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-06 2012-06-01T00:00:00Z |
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/1822/20485 |
url |
http://hdl.handle.net/1822/20485 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1793-5571 10.1142/S1793557112500180 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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132487427817472 |