The completion problem for N-matrices
Autor(a) principal: | |
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Data de Publicação: | 2002 |
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/1822/1456 |
Resumo: | An $n\times m$ 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 has 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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The completion problem for N-matricesPartial matrixMatrix completion problemN-matrixChordal graphsCyclesAn $n\times m$ 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 has 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) DGI - BFM2001-0081-C03-02World Scientific and Engineering Academy and Society (WSEAS)Universidade do MinhoAraújo, C. MendesTorregrosa, Juan R.20022002-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/1456eng"WSEAS transactions on mathematics". ISSN 1109-2769. 1:1/4 (2002) 53-58.info: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:RCAAP2023-07-21T12:24:48Zoai:repositorium.sdum.uminho.pt:1822/1456Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:18:53.688676Repositório 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 completion problem for N-matrices |
title |
The completion problem for N-matrices |
spellingShingle |
The completion problem for N-matrices Araújo, C. Mendes Partial matrix Matrix completion problem N-matrix Chordal graphs Cycles |
title_short |
The completion problem for N-matrices |
title_full |
The completion problem for N-matrices |
title_fullStr |
The completion problem for N-matrices |
title_full_unstemmed |
The completion problem for N-matrices |
title_sort |
The completion problem for N-matrices |
author |
Araújo, C. Mendes |
author_facet |
Araújo, C. Mendes Torregrosa, Juan R. |
author_role |
author |
author2 |
Torregrosa, Juan R. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Araújo, C. Mendes Torregrosa, Juan R. |
dc.subject.por.fl_str_mv |
Partial matrix Matrix completion problem N-matrix Chordal graphs Cycles |
topic |
Partial matrix Matrix completion problem N-matrix Chordal graphs Cycles |
description |
An $n\times m$ 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 has 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 |
2002 |
dc.date.none.fl_str_mv |
2002 2002-01-01T00:00:00Z |
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/1822/1456 |
url |
http://hdl.handle.net/1822/1456 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
"WSEAS transactions on mathematics". ISSN 1109-2769. 1:1/4 (2002) 53-58. |
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 |
World Scientific and Engineering Academy and Society (WSEAS) |
publisher.none.fl_str_mv |
World Scientific and Engineering Academy and Society (WSEAS) |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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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) |
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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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