Polytopes of Minimum Positive Semidefinite Rank
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2013 |
| 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/10316/44190 https://doi.org/10.1007/s00454-013-9533-x |
Resumo: | The positive semidefinite (psd) rank of a polytope is the smallest k for which the cone of k×k real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals this lower bound. We give several classes of polytopes that achieve the minimum possible psd rank including a complete characterization in dimensions two and three. |
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Polytopes of Minimum Positive Semidefinite RankThe positive semidefinite (psd) rank of a polytope is the smallest k for which the cone of k×k real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals this lower bound. We give several classes of polytopes that achieve the minimum possible psd rank including a complete characterization in dimensions two and three.Springer2013info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44190http://hdl.handle.net/10316/44190https://doi.org/10.1007/s00454-013-9533-xhttps://doi.org/10.1007/s00454-013-9533-xenghttps://doi.org/10.1007/s00454-013-9533-xGouveia, JoãoRobinson, Richard Z.Thomas, Rekha R.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:RCAAP2021-06-29T10:02:51Zoai:estudogeral.uc.pt:10316/44190Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:31.984999Repositório 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 |
Polytopes of Minimum Positive Semidefinite Rank |
| title |
Polytopes of Minimum Positive Semidefinite Rank |
| spellingShingle |
Polytopes of Minimum Positive Semidefinite Rank Gouveia, João |
| title_short |
Polytopes of Minimum Positive Semidefinite Rank |
| title_full |
Polytopes of Minimum Positive Semidefinite Rank |
| title_fullStr |
Polytopes of Minimum Positive Semidefinite Rank |
| title_full_unstemmed |
Polytopes of Minimum Positive Semidefinite Rank |
| title_sort |
Polytopes of Minimum Positive Semidefinite Rank |
| author |
Gouveia, João |
| author_facet |
Gouveia, João Robinson, Richard Z. Thomas, Rekha R. |
| author_role |
author |
| author2 |
Robinson, Richard Z. Thomas, Rekha R. |
| author2_role |
author author |
| dc.contributor.author.fl_str_mv |
Gouveia, João Robinson, Richard Z. Thomas, Rekha R. |
| description |
The positive semidefinite (psd) rank of a polytope is the smallest k for which the cone of k×k real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals this lower bound. We give several classes of polytopes that achieve the minimum possible psd rank including a complete characterization in dimensions two and three. |
| publishDate |
2013 |
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2013 |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/article |
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article |
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publishedVersion |
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http://hdl.handle.net/10316/44190 http://hdl.handle.net/10316/44190 https://doi.org/10.1007/s00454-013-9533-x https://doi.org/10.1007/s00454-013-9533-x |
| url |
http://hdl.handle.net/10316/44190 https://doi.org/10.1007/s00454-013-9533-x |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
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https://doi.org/10.1007/s00454-013-9533-x |
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info:eu-repo/semantics/openAccess |
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openAccess |
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Springer |
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Springer |
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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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