Sums and products of symplectic eigenvalues

Tanvi Jain

paper

Sums and products of symplectic eigenvalues

arXiv:2108.10741

Abstract

For every $2 n \times 2 n$ real positive definite matrix $A,$ there exists a real symplectic matrix $M$ such that $M^TAM=\diag(D,D),$ where $D$ is the $n \times n$ positive diagonal matrix with diagonal entries $d_{1} (A) \leq \dots \leq d_{n} (A) .$ The numbers $d_{1} (A), \dots, d_{n} (A)$ are called the symplectic eigenvalues of $A .$ We derive analogues of Wielandt's extremal principle and multiplicative Lidskii's inequalities for symplectic eigenvalues.