The Parter-Wiener theorem: Refinement and generalization
Autor(a) principal: | |
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Data de Publicação: | 2004 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10362/58383 |
Resumo: | An important theorem about the existence of principal submatrices of a Hermitian matrixwhose graph is a tree, in which the multiplicity of an eigenvalue increases, was largely developed in separate papers by Parter and Wiener. Here, the prior work is fully stated, then generalized with a self-contained proof. The more complete result is then used to better understand the eigenvalue possibilities of reducible principal submatrices of Hermitian tridiagonal matrices. Sets of vertices, for which the multiplicity increases, are also studied. |
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The Parter-Wiener theorem: Refinement and generalizationEigenvaluesHermitian matrixMultiplicityParter verticesTreeVertex degreesAn important theorem about the existence of principal submatrices of a Hermitian matrixwhose graph is a tree, in which the multiplicity of an eigenvalue increases, was largely developed in separate papers by Parter and Wiener. Here, the prior work is fully stated, then generalized with a self-contained proof. The more complete result is then used to better understand the eigenvalue possibilities of reducible principal submatrices of Hermitian tridiagonal matrices. Sets of vertices, for which the multiplicity increases, are also studied.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNJohnson, Charles R.Leal-Duarte, AntónioSaiago, Carlos Manuel2019-01-23T23:19:29Z20042004-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article10application/pdfhttp://hdl.handle.net/10362/58383eng0895-4798PURE: 353861https://doi.org/10.1137/S0895479801393320info: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:RCAAP2024-03-11T04:28:11Zoai:run.unl.pt:10362/58383Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:33:15.830332Repositório 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 Parter-Wiener theorem: Refinement and generalization |
title |
The Parter-Wiener theorem: Refinement and generalization |
spellingShingle |
The Parter-Wiener theorem: Refinement and generalization Johnson, Charles R. Eigenvalues Hermitian matrix Multiplicity Parter vertices Tree Vertex degrees |
title_short |
The Parter-Wiener theorem: Refinement and generalization |
title_full |
The Parter-Wiener theorem: Refinement and generalization |
title_fullStr |
The Parter-Wiener theorem: Refinement and generalization |
title_full_unstemmed |
The Parter-Wiener theorem: Refinement and generalization |
title_sort |
The Parter-Wiener theorem: Refinement and generalization |
author |
Johnson, Charles R. |
author_facet |
Johnson, Charles R. Leal-Duarte, António Saiago, Carlos Manuel |
author_role |
author |
author2 |
Leal-Duarte, António Saiago, Carlos Manuel |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
CMA - Centro de Matemática e Aplicações DM - Departamento de Matemática RUN |
dc.contributor.author.fl_str_mv |
Johnson, Charles R. Leal-Duarte, António Saiago, Carlos Manuel |
dc.subject.por.fl_str_mv |
Eigenvalues Hermitian matrix Multiplicity Parter vertices Tree Vertex degrees |
topic |
Eigenvalues Hermitian matrix Multiplicity Parter vertices Tree Vertex degrees |
description |
An important theorem about the existence of principal submatrices of a Hermitian matrixwhose graph is a tree, in which the multiplicity of an eigenvalue increases, was largely developed in separate papers by Parter and Wiener. Here, the prior work is fully stated, then generalized with a self-contained proof. The more complete result is then used to better understand the eigenvalue possibilities of reducible principal submatrices of Hermitian tridiagonal matrices. Sets of vertices, for which the multiplicity increases, are also studied. |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004 2004-01-01T00:00:00Z 2019-01-23T23:19:29Z |
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/10362/58383 |
url |
http://hdl.handle.net/10362/58383 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0895-4798 PURE: 353861 https://doi.org/10.1137/S0895479801393320 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
10 application/pdf |
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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1799137954255339520 |