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/10400.6/9625 |
Resumo: | Let T be a tree with n≥2 vertices. Set S(T) for the set of all real symmetric matrices whose graph is T. Let A∈S(T) and i∈{1,…,n} . We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set mA(i)(0)=mA(0)+1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B∈S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A∈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∈S(T) with b P-vertices and maximum nullity. |
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The number of P-vertices in a matrix with maximum nullityTreesParter verticesMaximum nullityLet T be a tree with n≥2 vertices. Set S(T) for the set of all real symmetric matrices whose graph is T. Let A∈S(T) and i∈{1,…,n} . We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set mA(i)(0)=mA(0)+1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B∈S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A∈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∈S(T) with b P-vertices and maximum nullity.ElsevieruBibliorumFernandes, RosárioCruz, Henrique F. Da2018-06-152024-06-15T00:00:00Z2018-06-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.6/9625eng10.1016/j.laa.2018.02.018info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-12-15T09:50:36Zoai:ubibliorum.ubi.pt:10400.6/9625Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:49:37.504370Repositório 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, Rosário Trees Parter vertices Maximum nullity |
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, Rosário |
author_facet |
Fernandes, Rosário Cruz, Henrique F. Da |
author_role |
author |
author2 |
Cruz, Henrique F. Da |
author2_role |
author |
dc.contributor.none.fl_str_mv |
uBibliorum |
dc.contributor.author.fl_str_mv |
Fernandes, Rosário Cruz, Henrique F. Da |
dc.subject.por.fl_str_mv |
Trees Parter vertices Maximum nullity |
topic |
Trees Parter vertices Maximum nullity |
description |
Let T be a tree with n≥2 vertices. Set S(T) for the set of all real symmetric matrices whose graph is T. Let A∈S(T) and i∈{1,…,n} . We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set mA(i)(0)=mA(0)+1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B∈S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A∈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∈S(T) with b P-vertices and maximum nullity. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-06-15 2018-06-15T00:00:00Z 2024-06-15T00:00:00Z |
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/10400.6/9625 |
url |
http://hdl.handle.net/10400.6/9625 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1016/j.laa.2018.02.018 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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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1799136387820158976 |