Matches in DBpedia 2015-10 for { ?s ?p "In mathematics, Kostant's convexity theorem, introduced by Bertram Kostant (1973), states that the projection of every coadjoint orbit of a connected compact Lie group into the dual of a Cartan subalgebra is a convex set. It is a special case of a more general result for symmetric spaces. Kostant's theorem is a generalization of a result of Schur (1923), Horn (1954) and Thompson (1972) for hermitian matrices. They proved that the projection onto the diagonal matrices of the space of all n by n complex self-adjoint matrices with given eigenvalues Λ = (λ1, ..., λn) is the convex polytope with vertices all permutations of the coordinates of Λ. In fact this result is 'Kostant's linear convexity theorem'; the main focus of Kostant (1973) is Kostant's nonlinear convexity theorem which involves the Iwasawa projection rather than the linear projection to the dual of a Cartan subalgebra.Kostant used this to generalize the Golden–Thompson inequality to all compact groups."@en }
Showing triples 1 to 1 of
1
with 100 triples per page.
- Kostants_convexity_theorem abstract "In mathematics, Kostant's convexity theorem, introduced by Bertram Kostant (1973), states that the projection of every coadjoint orbit of a connected compact Lie group into the dual of a Cartan subalgebra is a convex set. It is a special case of a more general result for symmetric spaces. Kostant's theorem is a generalization of a result of Schur (1923), Horn (1954) and Thompson (1972) for hermitian matrices. They proved that the projection onto the diagonal matrices of the space of all n by n complex self-adjoint matrices with given eigenvalues Λ = (λ1, ..., λn) is the convex polytope with vertices all permutations of the coordinates of Λ. In fact this result is 'Kostant's linear convexity theorem'; the main focus of Kostant (1973) is Kostant's nonlinear convexity theorem which involves the Iwasawa projection rather than the linear projection to the dual of a Cartan subalgebra.Kostant used this to generalize the Golden–Thompson inequality to all compact groups.".