The Parter-Wiener theorem: Refinement and generalization

Detalhes bibliográficos
Autor(a) principal: Johnson, Charles R.
Data de Publicação: 2004
Outros Autores: Leal-Duarte, António, Saiago, Carlos Manuel
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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spelling 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
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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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