Change in vertex status after removal of another vertex in the general setting
Autor(a) principal: | |
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Data de Publicação: | 2021 |
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/10362/135559 |
Resumo: | In the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded. |
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Change in vertex status after removal of another vertex in the general settingCombinatorially symmetricEigenvalueGeometric multiplicityGraph of a matrixTreeAlgebra and Number TheoryNumerical AnalysisGeometry and TopologyDiscrete Mathematics and CombinatoricsIn the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNJohnson, Charles R.Saiago, Carlos M.Toyonaga, Kenji2022-12-17T01:31:38Z2021-03-012021-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article18application/pdfhttp://hdl.handle.net/10362/135559eng0024-3795PURE: 27629983https://doi.org/10.1016/j.laa.2020.11.023info: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:RCAAP2024-03-11T05:13:56Zoai:run.unl.pt:10362/135559Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:48:27.263671Repositório 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 |
Change in vertex status after removal of another vertex in the general setting |
title |
Change in vertex status after removal of another vertex in the general setting |
spellingShingle |
Change in vertex status after removal of another vertex in the general setting Johnson, Charles R. Combinatorially symmetric Eigenvalue Geometric multiplicity Graph of a matrix Tree Algebra and Number Theory Numerical Analysis Geometry and Topology Discrete Mathematics and Combinatorics |
title_short |
Change in vertex status after removal of another vertex in the general setting |
title_full |
Change in vertex status after removal of another vertex in the general setting |
title_fullStr |
Change in vertex status after removal of another vertex in the general setting |
title_full_unstemmed |
Change in vertex status after removal of another vertex in the general setting |
title_sort |
Change in vertex status after removal of another vertex in the general setting |
author |
Johnson, Charles R. |
author_facet |
Johnson, Charles R. Saiago, Carlos M. Toyonaga, Kenji |
author_role |
author |
author2 |
Saiago, Carlos M. Toyonaga, Kenji |
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. Saiago, Carlos M. Toyonaga, Kenji |
dc.subject.por.fl_str_mv |
Combinatorially symmetric Eigenvalue Geometric multiplicity Graph of a matrix Tree Algebra and Number Theory Numerical Analysis Geometry and Topology Discrete Mathematics and Combinatorics |
topic |
Combinatorially symmetric Eigenvalue Geometric multiplicity Graph of a matrix Tree Algebra and Number Theory Numerical Analysis Geometry and Topology Discrete Mathematics and Combinatorics |
description |
In the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-03-01 2021-03-01T00:00:00Z 2022-12-17T01:31:38Z |
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/10362/135559 |
url |
http://hdl.handle.net/10362/135559 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0024-3795 PURE: 27629983 https://doi.org/10.1016/j.laa.2020.11.023 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
18 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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1799138085558026240 |