Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments

Detalhes bibliográficos
Autor(a) principal: Saiago, Carlos M.
Data de Publicação: 2019
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/100879
Resumo: UID/MAT/00297/2019
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spelling Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignmentsAssignmentsBranch duplicationCombinatorially symmetricDiagonalizable matrixDiameterEigenvalueGeometric multiplicityGraph of a matrixTreeAlgebra and Number TheoryGeometry and TopologyUID/MAT/00297/2019Considered are combinatorially symmetric matrices, whose graph is a given tree, in view of the fact recent analysis shows that the geometric multiplicity theory for the eigenvalues of such matrices closely parallels that for real symmetric (and complex Hermitian) matrices. In contrast to the real symmetric case, it is shown that (a) the smallest example (13 vertices) of a tree and multiplicity list (3, 3, 3, 1, 1, 1, 1) meeting standard necessary conditions that has no real symmetric realizations does have a diagonalizable realization and for arbitrary prescribed (real and multiple) eigenvalues, and (b) that all trees with diameter < 8 are geometrically di-minimal (i.e., have diagonalizable realizations with as few of distinct eigenvalues as the diameter). This re-raises natural questions about multiplicity lists that proved subtly false in the real symmetric case. What is their status in the geometric multiplicity list case?CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNSaiago, Carlos M.2020-07-14T22:19:27Z2019-01-012019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article11application/pdfhttp://hdl.handle.net/10362/100879eng2300-7451PURE: 17193935https://doi.org/10.1515/spma-2019-0025info: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:RCAAP2024-03-11T04:47:13Zoai:run.unl.pt:10362/100879Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:39:26.799621Repositório 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 Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments
title Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments
spellingShingle Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments
Saiago, Carlos M.
Assignments
Branch duplication
Combinatorially symmetric
Diagonalizable matrix
Diameter
Eigenvalue
Geometric multiplicity
Graph of a matrix
Tree
Algebra and Number Theory
Geometry and Topology
title_short Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments
title_full Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments
title_fullStr Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments
title_full_unstemmed Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments
title_sort Diagonalizable matrices whose graph is a tree: The minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments
author Saiago, Carlos M.
author_facet Saiago, Carlos M.
author_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Saiago, Carlos M.
dc.subject.por.fl_str_mv Assignments
Branch duplication
Combinatorially symmetric
Diagonalizable matrix
Diameter
Eigenvalue
Geometric multiplicity
Graph of a matrix
Tree
Algebra and Number Theory
Geometry and Topology
topic Assignments
Branch duplication
Combinatorially symmetric
Diagonalizable matrix
Diameter
Eigenvalue
Geometric multiplicity
Graph of a matrix
Tree
Algebra and Number Theory
Geometry and Topology
description UID/MAT/00297/2019
publishDate 2019
dc.date.none.fl_str_mv 2019-01-01
2019-01-01T00:00:00Z
2020-07-14T22:19:27Z
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/10362/100879
url http://hdl.handle.net/10362/100879
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2300-7451
PURE: 17193935
https://doi.org/10.1515/spma-2019-0025
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 11
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
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