Matches in SemOpenAlex for { <https://semopenalex.org/work/W2956038953> ?p ?o ?g. }
Showing items 1 to 92 of
92
with 100 items per page.
- W2956038953 abstract "Consider the Lie group of n x n complex unitary matrices U(n) endowed with the bi-invariant Finsler metric given by the spectral norm, ||X||_U = ||U*X||_{sp} = ||X||_{sp} for any X tangent to a unitary operator U. Given two points in U(n), in general there exists infinitely many curves of minimal length. The aim of this paper is to provide a complete description of such curves. As a consequence of this description, we conclude that there is a unique curve of minimal length between U and V if and only if the spectrum of U*V is contained in a set of the form {e^{i theta}, e^{-i theta}} for some theta in [0, infty). Similar studies are done for the Grassmann manifolds. Now consider the cone of n x n positive invertible matrices Gl(n)+ endowed with the bi-invariant Finsler metric given by the trace norm, ||X||_{1, A} = ||A^{-1/2}XA^{-1/2}||_1 for any X tangent to A in Gl(n)+. In this context, given two points A,B in Gl(n)+ there exists infinitely many curves of minimal length. In order to provide a complete description of such curves, we provide a characterization of the minimal curves joining two Hermitian matrices X, Y in H(n). As a consequence of the last description, we provide a way to construct minimal paths in the group of unitary matrices U(n) endowed with the bi-invariant Finsler metric ||X||_{1, U} = ||U*X||_{1} = ||X||_{1} for any X tangent to U in U(n). We also study the set of intermediate points in all the previous contexts. Between two given unitary matrices U and V we prove that this set is geodesically convex provided ||U - V||_{sp} < 1. In Gl(n)+ this set is geodesically convex for every unitarily invariant norm." @default.
- W2956038953 created "2019-07-12" @default.
- W2956038953 creator A5016971815 @default.
- W2956038953 creator A5050950631 @default.
- W2956038953 creator A5052070210 @default.
- W2956038953 date "2019-07-07" @default.
- W2956038953 modified "2023-10-06" @default.
- W2956038953 title "Minimal curves in U(n) and Gl(n)+ with respect to the spectral and the trace norms" @default.
- W2956038953 cites W1970377488 @default.
- W2956038953 cites W1983051686 @default.
- W2956038953 cites W1996886518 @default.
- W2956038953 cites W2000893081 @default.
- W2956038953 cites W2020413305 @default.
- W2956038953 cites W2046594877 @default.
- W2956038953 cites W2049460183 @default.
- W2956038953 cites W2070319354 @default.
- W2956038953 cites W2074571557 @default.
- W2956038953 cites W2078801781 @default.
- W2956038953 cites W2083054109 @default.
- W2956038953 cites W2223353064 @default.
- W2956038953 cites W2270302920 @default.
- W2956038953 cites W2798707604 @default.
- W2956038953 cites W585133165 @default.
- W2956038953 cites W91382447 @default.
- W2956038953 cites W1993862123 @default.
- W2956038953 cites W2011568044 @default.
- W2956038953 hasPublicationYear "2019" @default.
- W2956038953 type Work @default.
- W2956038953 sameAs 2956038953 @default.
- W2956038953 citedByCount "1" @default.
- W2956038953 countsByYear W29560389532023 @default.
- W2956038953 crossrefType "posted-content" @default.
- W2956038953 hasAuthorship W2956038953A5016971815 @default.
- W2956038953 hasAuthorship W2956038953A5050950631 @default.
- W2956038953 hasAuthorship W2956038953A5052070210 @default.
- W2956038953 hasConcept C114614502 @default.
- W2956038953 hasConcept C138885662 @default.
- W2956038953 hasConcept C163353815 @default.
- W2956038953 hasConcept C17744445 @default.
- W2956038953 hasConcept C190470478 @default.
- W2956038953 hasConcept C199539241 @default.
- W2956038953 hasConcept C202444582 @default.
- W2956038953 hasConcept C33923547 @default.
- W2956038953 hasConcept C37914503 @default.
- W2956038953 hasConcept C41895202 @default.
- W2956038953 hasConcept C67820243 @default.
- W2956038953 hasConcept C75291252 @default.
- W2956038953 hasConcept C94940 @default.
- W2956038953 hasConcept C96442724 @default.
- W2956038953 hasConcept C99072794 @default.
- W2956038953 hasConceptScore W2956038953C114614502 @default.
- W2956038953 hasConceptScore W2956038953C138885662 @default.
- W2956038953 hasConceptScore W2956038953C163353815 @default.
- W2956038953 hasConceptScore W2956038953C17744445 @default.
- W2956038953 hasConceptScore W2956038953C190470478 @default.
- W2956038953 hasConceptScore W2956038953C199539241 @default.
- W2956038953 hasConceptScore W2956038953C202444582 @default.
- W2956038953 hasConceptScore W2956038953C33923547 @default.
- W2956038953 hasConceptScore W2956038953C37914503 @default.
- W2956038953 hasConceptScore W2956038953C41895202 @default.
- W2956038953 hasConceptScore W2956038953C67820243 @default.
- W2956038953 hasConceptScore W2956038953C75291252 @default.
- W2956038953 hasConceptScore W2956038953C94940 @default.
- W2956038953 hasConceptScore W2956038953C96442724 @default.
- W2956038953 hasConceptScore W2956038953C99072794 @default.
- W2956038953 hasLocation W29560389531 @default.
- W2956038953 hasOpenAccess W2956038953 @default.
- W2956038953 hasPrimaryLocation W29560389531 @default.
- W2956038953 hasRelatedWork W2006782083 @default.
- W2956038953 hasRelatedWork W2052855897 @default.
- W2956038953 hasRelatedWork W2110012166 @default.
- W2956038953 hasRelatedWork W2225477864 @default.
- W2956038953 hasRelatedWork W2233011262 @default.
- W2956038953 hasRelatedWork W2263550119 @default.
- W2956038953 hasRelatedWork W2572208251 @default.
- W2956038953 hasRelatedWork W2768687568 @default.
- W2956038953 hasRelatedWork W2914287831 @default.
- W2956038953 hasRelatedWork W2930346063 @default.
- W2956038953 hasRelatedWork W2950090378 @default.
- W2956038953 hasRelatedWork W2951913466 @default.
- W2956038953 hasRelatedWork W2963297777 @default.
- W2956038953 hasRelatedWork W2963633236 @default.
- W2956038953 hasRelatedWork W2963879158 @default.
- W2956038953 hasRelatedWork W2986765257 @default.
- W2956038953 hasRelatedWork W3022476541 @default.
- W2956038953 hasRelatedWork W3101027378 @default.
- W2956038953 hasRelatedWork W3142960981 @default.
- W2956038953 hasRelatedWork W3184202161 @default.
- W2956038953 isParatext "false" @default.
- W2956038953 isRetracted "false" @default.
- W2956038953 magId "2956038953" @default.
- W2956038953 workType "article" @default.