Geometric proofs of some theorems of Schur-Horn type
New geometric proofs of some theorems in linear algebra are given. Firstly, the classical Schur-Horn theorem for real symmetric (resp. Hermitian) matrices is proved. Secondly, a less known Schur-Horn theorem for skew-symmetric matrices is proved by geometric methods. Standard symplectic arguments are used to obtain two complex counterparts of this theorem. It is emphasized that some elements of the authors' geometric proofs are familiar to the closely related subjects of Coxeter groups and Lie algebras; the authors' conclusion is that their results can be special cases of a more general theorem. Finally, the geometric techniques are used to prove Horn's characterization of the diagonal entries of orthogonal matrices.
scientific article; zbMATH DE number 1331730
scientific article