The N-matrix completion problem under digraphs assumptions
Autor(a) principal: | |
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Data de Publicação: | 2004 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/1822/2870 |
Resumo: | An $n \times n$ matrix is called an $N$--matrix if all principal minors are negative. In this paper, we are interested in the partial $N$--matrix completion problem, when the partial $N$--matrix is non-combinatorially symmetric. In general, this type of partial matrices does not have an $N$--matrix completion. We prove that a non-combinatorially symmetric partial $N$--matrix has an $N$--matrix completion if the graph of its specified entries is an acyclic graph or a cycle. We also prove that there exists the desired completion for partial $N$--matrices such that in its associated graphs the cycles play an important role. |
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The N-matrix completion problem under digraphs assumptionsPartial matrixMatrix completion problemsN-matrixDigraphcompletion problemdirected graphsScience & TechnologyAn $n \times n$ matrix is called an $N$--matrix if all principal minors are negative. In this paper, we are interested in the partial $N$--matrix completion problem, when the partial $N$--matrix is non-combinatorially symmetric. In general, this type of partial matrices does not have an $N$--matrix completion. We prove that a non-combinatorially symmetric partial $N$--matrix has an $N$--matrix completion if the graph of its specified entries is an acyclic graph or a cycle. We also prove that there exists the desired completion for partial $N$--matrices such that in its associated graphs the cycles play an important role.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação" (POCTI). Spanish DGI - grant number BFM2001-0081-C03-02.ElsevierUniversidade do MinhoAraújo, C. MendesTorregrosa, Juan R.Urbano, Ana M.2004-03-152004-03-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/2870engMendes Araújo, C., Torregrosa, J. R., & Urbano, A. M. (2004, March). The N-matrix completion problem under digraphs assumptions. Linear Algebra and its Applications. Elsevier BV. http://doi.org/10.1016/j.laa.2003.10.0170024-379510.1016/j.laa.2003.10.017www.sciencedirect.cominfo: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:RCAAP2023-07-21T12:07:21Zoai:repositorium.sdum.uminho.pt:1822/2870Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:58:16.304970Repositório 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 N-matrix completion problem under digraphs assumptions |
title |
The N-matrix completion problem under digraphs assumptions |
spellingShingle |
The N-matrix completion problem under digraphs assumptions Araújo, C. Mendes Partial matrix Matrix completion problems N-matrix Digraph completion problem directed graphs Science & Technology |
title_short |
The N-matrix completion problem under digraphs assumptions |
title_full |
The N-matrix completion problem under digraphs assumptions |
title_fullStr |
The N-matrix completion problem under digraphs assumptions |
title_full_unstemmed |
The N-matrix completion problem under digraphs assumptions |
title_sort |
The N-matrix completion problem under digraphs assumptions |
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 problems N-matrix Digraph completion problem directed graphs Science & Technology |
topic |
Partial matrix Matrix completion problems N-matrix Digraph completion problem directed graphs Science & Technology |
description |
An $n \times n$ matrix is called an $N$--matrix if all principal minors are negative. In this paper, we are interested in the partial $N$--matrix completion problem, when the partial $N$--matrix is non-combinatorially symmetric. In general, this type of partial matrices does not have an $N$--matrix completion. We prove that a non-combinatorially symmetric partial $N$--matrix has an $N$--matrix completion if the graph of its specified entries is an acyclic graph or a cycle. We also prove that there exists the desired completion for partial $N$--matrices such that in its associated graphs the cycles play an important role. |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004-03-15 2004-03-15T00:00:00Z |
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 |
https://hdl.handle.net/1822/2870 |
url |
https://hdl.handle.net/1822/2870 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Mendes Araújo, C., Torregrosa, J. R., & Urbano, A. M. (2004, March). The N-matrix completion problem under digraphs assumptions. Linear Algebra and its Applications. Elsevier BV. http://doi.org/10.1016/j.laa.2003.10.017 0024-3795 10.1016/j.laa.2003.10.017 www.sciencedirect.com |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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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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