Sums and products of symplectic eigenvalues
Linear Algebra and Its Applications
For every 2n×2n real positive definite matrix A, there exists a real symplectic matrix M such that MTAM=diag(D,D), where D is the n×n positive diagonal matrix with diagonal entries d1(A)≤⋯≤dn(A). The numbers d1(A),…,dn(A) are called the symplectic eigenvalues of A. We derive analogues of Wielandt's extremal principle and multiplicative Lidskii's inequalities for symplectic eigenvalues.
Jain, Tanvi, "Sums and products of symplectic eigenvalues" (2021). Journal Articles. 1651.
Open Access, Green