Positive semidefinite rank
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2015 |
| 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/10316/44191 https://doi.org/10.1007/s10107-015-0922-1 |
Resumo: | Let M∈R^p×q be a nonnegative matrix. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices A_i, B_j of size k × k such that M_ij = trace(A_i B_j). The psd rank has many appealing geometric interpretations, including semidefinite representations of polyhedra and information-theoretic applications. In this paper we develop and survey the main mathematical properties of psd rank, including its geometry, relationships with other rank notions, and computational and algorithmic aspects. |
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Positive semidefinite rankLet M∈R^p×q be a nonnegative matrix. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices A_i, B_j of size k × k such that M_ij = trace(A_i B_j). The psd rank has many appealing geometric interpretations, including semidefinite representations of polyhedra and information-theoretic applications. In this paper we develop and survey the main mathematical properties of psd rank, including its geometry, relationships with other rank notions, and computational and algorithmic aspects.Springer2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44191http://hdl.handle.net/10316/44191https://doi.org/10.1007/s10107-015-0922-1https://doi.org/10.1007/s10107-015-0922-1enghttps://doi.org/10.1007/s10107-015-0922-1Fawzi, HamzaGouveia, JoãoParrilo, Pablo A.Robinson, 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:RCAAP2021-06-29T10:02:52Zoai:estudogeral.uc.pt:10316/44191Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:31.737969Repositório 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 |
Positive semidefinite rank |
| title |
Positive semidefinite rank |
| spellingShingle |
Positive semidefinite rank Fawzi, Hamza |
| title_short |
Positive semidefinite rank |
| title_full |
Positive semidefinite rank |
| title_fullStr |
Positive semidefinite rank |
| title_full_unstemmed |
Positive semidefinite rank |
| title_sort |
Positive semidefinite rank |
| author |
Fawzi, Hamza |
| author_facet |
Fawzi, Hamza Gouveia, João Parrilo, Pablo A. Robinson, Richard Z. Thomas, Rekha R. |
| author_role |
author |
| author2 |
Gouveia, João Parrilo, Pablo A. Robinson, Richard Z. Thomas, Rekha R. |
| author2_role |
author author author author |
| dc.contributor.author.fl_str_mv |
Fawzi, Hamza Gouveia, João Parrilo, Pablo A. Robinson, Richard Z. Thomas, Rekha R. |
| description |
Let M∈R^p×q be a nonnegative matrix. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices A_i, B_j of size k × k such that M_ij = trace(A_i B_j). The psd rank has many appealing geometric interpretations, including semidefinite representations of polyhedra and information-theoretic applications. In this paper we develop and survey the main mathematical properties of psd rank, including its geometry, relationships with other rank notions, and computational and algorithmic aspects. |
| publishDate |
2015 |
| dc.date.none.fl_str_mv |
2015 |
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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 |
| dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/44191 http://hdl.handle.net/10316/44191 https://doi.org/10.1007/s10107-015-0922-1 https://doi.org/10.1007/s10107-015-0922-1 |
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http://hdl.handle.net/10316/44191 https://doi.org/10.1007/s10107-015-0922-1 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
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https://doi.org/10.1007/s10107-015-0922-1 |
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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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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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