Sums and products of symplectic eigenvalues

2021/08/24 by Jain, Tanvi
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2108.10741

Abstract

For every 2n× 2n real positive definite matrix A, there exists a real symplectic matrix M such that M^TAM=\diag(D,D), where D is the n× n positive diagonal matrix with diagonal entries d₁(A)≤ ⋯≤ d_n(A). The numbers d₁(A),…,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.

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