Singular values and eigenvalues of matrices in $\mathfrak{so}_n(\mathbb{C})$ and $\mathfrak{sp}_n(\mathbb{C})$

Abstract

We give a complete relation between the singular values and eigenvalues of a complex skew symmetric matrix in terms of multiplicative majorization and double occurrences of singular values and eigenvalues. Similar studies are given for matrices in the algebras $\mathfrak{sp}_n(\mathbb{C})$ and $\mathfrak{sp}_n(\mathbb{R})$.