N-matrix completion problem
Autor(a) principal: | |
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Data de Publicação: | 2003 |
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/1822/1471 |
Resumo: | An n x n matrix is called an N-matrix if all principal minors are negative. In this paper, we are interested in N-matrix completion problems, that is, when a partial N-matrix hás an N-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial N-matrix does not have an N-matrix completion. Here we prove that a combinatorially symmetric partial N-matrix has an N-matrix completion if the graph of its specified entries is a 1-chordal graph. We also prove that there exists an N-matrix completion for a partial N-matrix whose associated graph is an undirected cycle. |
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N-matrix completion problemPartial MatrixMatrix completion problemN-matrixUndirected graphscompletion problemundirected graphScience & TechnologyAn n x n matrix is called an N-matrix if all principal minors are negative. In this paper, we are interested in N-matrix completion problems, that is, when a partial N-matrix hás an N-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial N-matrix does not have an N-matrix completion. Here we prove that a combinatorially symmetric partial N-matrix has an N-matrix completion if the graph of its specified entries is a 1-chordal graph. We also prove that there exists an N-matrix completion for a partial N-matrix whose associated graph is an undirected cycle.Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI).ElsevierUniversidade do MinhoAraújo, C. MendesTorregrosa, Juan R.Urbano, Ana M.2003-10-012003-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/1471eng"Linear algebra and its applications". ISSN 0024-3795. 372 (2003) 111-125.0024-379510.1016/S0024-3795(03)00500-7info: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:RCAAP2023-07-21T12:30:54Zoai:repositorium.sdum.uminho.pt:1822/1471Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:26:09.753067Repositório 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 |
N-matrix completion problem |
title |
N-matrix completion problem |
spellingShingle |
N-matrix completion problem Araújo, C. Mendes Partial Matrix Matrix completion problem N-matrix Undirected graphs completion problem undirected graph Science & Technology |
title_short |
N-matrix completion problem |
title_full |
N-matrix completion problem |
title_fullStr |
N-matrix completion problem |
title_full_unstemmed |
N-matrix completion problem |
title_sort |
N-matrix completion problem |
author |
Araújo, C. Mendes |
author_facet |
Araújo, C. Mendes Torregrosa, Juan R. Urbano, Ana M. |
author_role |
author |
author2 |
Torregrosa, Juan R. Urbano, Ana M. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Araújo, C. Mendes Torregrosa, Juan R. Urbano, Ana M. |
dc.subject.por.fl_str_mv |
Partial Matrix Matrix completion problem N-matrix Undirected graphs completion problem undirected graph Science & Technology |
topic |
Partial Matrix Matrix completion problem N-matrix Undirected graphs completion problem undirected graph Science & Technology |
description |
An n x n matrix is called an N-matrix if all principal minors are negative. In this paper, we are interested in N-matrix completion problems, that is, when a partial N-matrix hás an N-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial N-matrix does not have an N-matrix completion. Here we prove that a combinatorially symmetric partial N-matrix has an N-matrix completion if the graph of its specified entries is a 1-chordal graph. We also prove that there exists an N-matrix completion for a partial N-matrix whose associated graph is an undirected cycle. |
publishDate |
2003 |
dc.date.none.fl_str_mv |
2003-10-01 2003-10-01T00:00:00Z |
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/1822/1471 |
url |
http://hdl.handle.net/1822/1471 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
"Linear algebra and its applications". ISSN 0024-3795. 372 (2003) 111-125. 0024-3795 10.1016/S0024-3795(03)00500-7 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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