Matches in SemOpenAlex for { <https://semopenalex.org/work/W2950597779> ?p ?o ?g. }
- W2950597779 abstract "The problem of finding a rank-one solution to a system of linear matrix equations arises from many practical applications. Given a system of linear matrix equations, however, such a low-rank solution does not always exist. In this paper, we aim at developing some sufficient conditions for the existence of a rank-one solution to the system of homogeneous linear matrix equations (HLME) over the positive semidefinite cone. First, we prove that an existence condition of a rank-one solution can be established by a homotopy invariance theorem. The derived condition is closely related to the so-called $P_emptyset$ property of the function defined by quadratic transformations. Second, we prove that the existence condition for a rank-one solution can be also established through the maximum rank of the (positive semidefinite) linear combination of given matrices. It is shown that an upper bound for the rank of the solution to a system of HLME over the positive semidefinite cone can be obtained efficiently by solving a semidefinite programming (SDP) problem. Moreover, a sufficient condition for the nonexistence of a rank-one solution to the system of HLME is also established in this paper." @default.
- W2950597779 created "2019-06-27" @default.
- W2950597779 creator A5057733991 @default.
- W2950597779 creator A5058813836 @default.
- W2950597779 date "2012-11-09" @default.
- W2950597779 modified "2023-09-24" @default.
- W2950597779 title "Rank-one Solutions for Homogeneous Linear Matrix Equations over the Positive Semidefinite Cone" @default.
- W2950597779 cites W1488435683 @default.
- W2950597779 cites W1490549637 @default.
- W2950597779 cites W1522995151 @default.
- W2950597779 cites W1603816954 @default.
- W2950597779 cites W1639316992 @default.
- W2950597779 cites W1964092554 @default.
- W2950597779 cites W1970670479 @default.
- W2950597779 cites W2000151369 @default.
- W2950597779 cites W2005037112 @default.
- W2950597779 cites W2005102197 @default.
- W2950597779 cites W2047386668 @default.
- W2950597779 cites W2054443446 @default.
- W2950597779 cites W2067785816 @default.
- W2950597779 cites W2067959964 @default.
- W2950597779 cites W2076622878 @default.
- W2950597779 cites W2077205953 @default.
- W2950597779 cites W2077242588 @default.
- W2950597779 cites W2080359169 @default.
- W2950597779 cites W2085377246 @default.
- W2950597779 cites W2093790790 @default.
- W2950597779 cites W2118550318 @default.
- W2950597779 cites W2128916604 @default.
- W2950597779 cites W2134332047 @default.
- W2950597779 cites W2140214428 @default.
- W2950597779 cites W2145096794 @default.
- W2950597779 cites W2161374719 @default.
- W2950597779 cites W2296319761 @default.
- W2950597779 cites W2296616510 @default.
- W2950597779 cites W2339666411 @default.
- W2950597779 cites W2478091498 @default.
- W2950597779 cites W2611328865 @default.
- W2950597779 cites W2949351217 @default.
- W2950597779 cites W2950358183 @default.
- W2950597779 cites W2963942504 @default.
- W2950597779 cites W3029645440 @default.
- W2950597779 cites W360528349 @default.
- W2950597779 cites W198837200 @default.
- W2950597779 doi "https://doi.org/10.48550/arxiv.1211.2131" @default.
- W2950597779 hasPublicationYear "2012" @default.
- W2950597779 type Work @default.
- W2950597779 sameAs 2950597779 @default.
- W2950597779 citedByCount "0" @default.
- W2950597779 crossrefType "posted-content" @default.
- W2950597779 hasAuthorship W2950597779A5057733991 @default.
- W2950597779 hasAuthorship W2950597779A5058813836 @default.
- W2950597779 hasBestOaLocation W29505977791 @default.
- W2950597779 hasConcept C101901036 @default.
- W2950597779 hasConcept C106487976 @default.
- W2950597779 hasConcept C11413529 @default.
- W2950597779 hasConcept C114614502 @default.
- W2950597779 hasConcept C121332964 @default.
- W2950597779 hasConcept C126255220 @default.
- W2950597779 hasConcept C134306372 @default.
- W2950597779 hasConcept C158693339 @default.
- W2950597779 hasConcept C159985019 @default.
- W2950597779 hasConcept C164226766 @default.
- W2950597779 hasConcept C192562407 @default.
- W2950597779 hasConcept C28826006 @default.
- W2950597779 hasConcept C30014739 @default.
- W2950597779 hasConcept C33923547 @default.
- W2950597779 hasConcept C49712288 @default.
- W2950597779 hasConcept C62520636 @default.
- W2950597779 hasConcept C94523830 @default.
- W2950597779 hasConceptScore W2950597779C101901036 @default.
- W2950597779 hasConceptScore W2950597779C106487976 @default.
- W2950597779 hasConceptScore W2950597779C11413529 @default.
- W2950597779 hasConceptScore W2950597779C114614502 @default.
- W2950597779 hasConceptScore W2950597779C121332964 @default.
- W2950597779 hasConceptScore W2950597779C126255220 @default.
- W2950597779 hasConceptScore W2950597779C134306372 @default.
- W2950597779 hasConceptScore W2950597779C158693339 @default.
- W2950597779 hasConceptScore W2950597779C159985019 @default.
- W2950597779 hasConceptScore W2950597779C164226766 @default.
- W2950597779 hasConceptScore W2950597779C192562407 @default.
- W2950597779 hasConceptScore W2950597779C28826006 @default.
- W2950597779 hasConceptScore W2950597779C30014739 @default.
- W2950597779 hasConceptScore W2950597779C33923547 @default.
- W2950597779 hasConceptScore W2950597779C49712288 @default.
- W2950597779 hasConceptScore W2950597779C62520636 @default.
- W2950597779 hasConceptScore W2950597779C94523830 @default.
- W2950597779 hasLocation W29505977791 @default.
- W2950597779 hasLocation W29505977792 @default.
- W2950597779 hasOpenAccess W2950597779 @default.
- W2950597779 hasPrimaryLocation W29505977791 @default.
- W2950597779 hasRelatedWork W1409680301 @default.
- W2950597779 hasRelatedWork W2000495681 @default.
- W2950597779 hasRelatedWork W2171800673 @default.
- W2950597779 hasRelatedWork W2182159254 @default.
- W2950597779 hasRelatedWork W2398847941 @default.
- W2950597779 hasRelatedWork W2950597779 @default.
- W2950597779 hasRelatedWork W2950697756 @default.
- W2950597779 hasRelatedWork W2982033561 @default.
- W2950597779 hasRelatedWork W3022946593 @default.