Orthosymplectic diagonalization in Williamson's theorem

Abstract

In this paper, we provide an algebraic condition on any $2n\times 2n$ real symmetric positive definite matrix which is necessary and sufficient for the matrix to be diagonalized by an orthosymplectic matrix in the sense of Williamson's theorem.

This work is going to become part of a bigger project that would contain wider applications of the main result presented in the paper