N_0 completions on partial matrices
Autor(a) principal: | |
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Data de Publicação: | 2009 |
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/1822/11155 |
Resumo: | An $n\times n$ matrix is called an $N_0$-matrix if all its principal minors are nonpositive. In this paper, we are interested in $N_0$-matrix completion problems, that is, when a partial $N_0$-matrix has an $N_0$-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial $N_0$-matrix does not have an $N_0$-matrix completion. Here, we prove that a combinatorially symmetric partial $N_0$-matrix, with no null main diagonal entries, has an $N_0$-matrix completion if the graph of its specified entries is a 1-chordal graph or a cycle. We also analyze the mentioned problem when the partial matrix has some null main diagonal entries. |
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spelling |
N_0 completions on partial matricesPartial matrixN_0-matrixCompletionChordal graphsCycleChordal graphN -matrix 0Science & TechnologyAn $n\times n$ matrix is called an $N_0$-matrix if all its principal minors are nonpositive. In this paper, we are interested in $N_0$-matrix completion problems, that is, when a partial $N_0$-matrix has an $N_0$-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial $N_0$-matrix does not have an $N_0$-matrix completion. Here, we prove that a combinatorially symmetric partial $N_0$-matrix, with no null main diagonal entries, has an $N_0$-matrix completion if the graph of its specified entries is a 1-chordal graph or a cycle. We also analyze the mentioned problem when the partial matrix has some null main diagonal entries.Fundação para a Ciência e a Tecnologia(FCT) através do programa POCTISpanish DGI grant number MTM2007-64477ElsevierUniversidade do MinhoAraújo, C. MendesTorregrosa, Juan R.Jordán, Cristina2009-05-152009-05-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/11155eng"Applied Mathematics and Computation". ISSN 0096-3003. 211:2 (May 2009) 303-312.0096-300310.1016/j.amc.2009.01.063http://www.sciencedirect.com/science/journal/00963003info: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:RCAAP2023-07-21T12:49:19Zoai:repositorium.sdum.uminho.pt:1822/11155Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:47:45.818085Repositório 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_0 completions on partial matrices |
title |
N_0 completions on partial matrices |
spellingShingle |
N_0 completions on partial matrices Araújo, C. Mendes Partial matrix N_0-matrix Completion Chordal graphs Cycle Chordal graph N -matrix 0 Science & Technology |
title_short |
N_0 completions on partial matrices |
title_full |
N_0 completions on partial matrices |
title_fullStr |
N_0 completions on partial matrices |
title_full_unstemmed |
N_0 completions on partial matrices |
title_sort |
N_0 completions on partial matrices |
author |
Araújo, C. Mendes |
author_facet |
Araújo, C. Mendes Torregrosa, Juan R. Jordán, Cristina |
author_role |
author |
author2 |
Torregrosa, Juan R. Jordán, Cristina |
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. Jordán, Cristina |
dc.subject.por.fl_str_mv |
Partial matrix N_0-matrix Completion Chordal graphs Cycle Chordal graph N -matrix 0 Science & Technology |
topic |
Partial matrix N_0-matrix Completion Chordal graphs Cycle Chordal graph N -matrix 0 Science & Technology |
description |
An $n\times n$ matrix is called an $N_0$-matrix if all its principal minors are nonpositive. In this paper, we are interested in $N_0$-matrix completion problems, that is, when a partial $N_0$-matrix has an $N_0$-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial $N_0$-matrix does not have an $N_0$-matrix completion. Here, we prove that a combinatorially symmetric partial $N_0$-matrix, with no null main diagonal entries, has an $N_0$-matrix completion if the graph of its specified entries is a 1-chordal graph or a cycle. We also analyze the mentioned problem when the partial matrix has some null main diagonal entries. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-05-15 2009-05-15T00:00:00Z |
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/1822/11155 |
url |
http://hdl.handle.net/1822/11155 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
"Applied Mathematics and Computation". ISSN 0096-3003. 211:2 (May 2009) 303-312. 0096-3003 10.1016/j.amc.2009.01.063 http://www.sciencedirect.com/science/journal/00963003 |
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 |
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) |
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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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1799133053184901120 |