Geometric proofs of some theorems of Schur-Horn type Original Research Article

We describe elementary, geometric proofs of the classical Schur-Horn theorem for symmetric matrices and analogous results for skew-symmetric matrices, in the real and complex cases. We compare this approach to the proofs obtained by making use of symplectic techniques. As a further application, we present a new proof of Hornʹs characterization of diagonal entries of orthogonal matrices.