The number of P-vertices in a matrix with maximum nullity
Autor(a) principal: | |
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Data de Publicação: | 2018 |
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/10362/64137 |
Resumo: | Let T be a tree with n >= 2 vertices. Set 8(T) for the set of all real symmetric matrices whose graph is T. Let A is an element of S(T) and i is an element of {1, . . . , n}. We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set m(A) (0) for the multiplicity of the eigenvalue zero in A (the nullity of A). When m(A(i)) (0) = m(A) (0) + 1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B is an element of S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A is an element of S(T) with nullity M(T). We also prove that if the integer b is between these two bounds, then there is a matrix E is an element of S(T) with b P-vertices and maximum nullity. (C) 2018 Elsevier Inc. All rights reserved. |
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7160 |
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The number of P-vertices in a matrix with maximum nullityTreesAcyclic matricesMaximum nullityParter verticesLet T be a tree with n >= 2 vertices. Set 8(T) for the set of all real symmetric matrices whose graph is T. Let A is an element of S(T) and i is an element of {1, . . . , n}. We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set m(A) (0) for the multiplicity of the eigenvalue zero in A (the nullity of A). When m(A(i)) (0) = m(A) (0) + 1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B is an element of S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A is an element of S(T) with nullity M(T). We also prove that if the integer b is between these two bounds, then there is a matrix E is an element of S(T) with b P-vertices and maximum nullity. (C) 2018 Elsevier Inc. All rights reserved.DM - Departamento de MatemáticaRUNFernandes, Maria do Rosário Silva Francoda Cruz, Henrique F.2019-03-21T23:15:49Z20182018-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article15application/pdfhttp://hdl.handle.net/10362/64137eng0024-3795PURE: 3808808info: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:RCAAP2024-03-11T04:30:27Zoai:run.unl.pt:10362/64137Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:34:05.398315Repositório 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 number of P-vertices in a matrix with maximum nullity |
title |
The number of P-vertices in a matrix with maximum nullity |
spellingShingle |
The number of P-vertices in a matrix with maximum nullity Fernandes, Maria do Rosário Silva Franco Trees Acyclic matrices Maximum nullity Parter vertices |
title_short |
The number of P-vertices in a matrix with maximum nullity |
title_full |
The number of P-vertices in a matrix with maximum nullity |
title_fullStr |
The number of P-vertices in a matrix with maximum nullity |
title_full_unstemmed |
The number of P-vertices in a matrix with maximum nullity |
title_sort |
The number of P-vertices in a matrix with maximum nullity |
author |
Fernandes, Maria do Rosário Silva Franco |
author_facet |
Fernandes, Maria do Rosário Silva Franco da Cruz, Henrique F. |
author_role |
author |
author2 |
da Cruz, Henrique F. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
DM - Departamento de Matemática RUN |
dc.contributor.author.fl_str_mv |
Fernandes, Maria do Rosário Silva Franco da Cruz, Henrique F. |
dc.subject.por.fl_str_mv |
Trees Acyclic matrices Maximum nullity Parter vertices |
topic |
Trees Acyclic matrices Maximum nullity Parter vertices |
description |
Let T be a tree with n >= 2 vertices. Set 8(T) for the set of all real symmetric matrices whose graph is T. Let A is an element of S(T) and i is an element of {1, . . . , n}. We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set m(A) (0) for the multiplicity of the eigenvalue zero in A (the nullity of A). When m(A(i)) (0) = m(A) (0) + 1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B is an element of S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A is an element of S(T) with nullity M(T). We also prove that if the integer b is between these two bounds, then there is a matrix E is an element of S(T) with b P-vertices and maximum nullity. (C) 2018 Elsevier Inc. All rights reserved. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018 2018-01-01T00:00:00Z 2019-03-21T23:15:49Z |
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/10362/64137 |
url |
http://hdl.handle.net/10362/64137 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0024-3795 PURE: 3808808 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
15 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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1799137962315743232 |