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arxiv: 1710.00494 · v1 · pith:4S5B6UNMnew · submitted 2017-10-02 · 🧮 math.FA · math.PR

Log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter

Fumio Hiai , Yongdo Lim This is my paper
classification 🧮 math.FA math.PR
keywords symplecticbarycentercartaneigenvalueeigenvaluesintegrablelog-majorizationsborel
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In this paper we show that the eigenvalue map and the symplectic eigenvalue map of positive definite matrices are Lipschitz for the Cartan-Hadamard Riemannian metric, and establish log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter of integrable probability Borel measures. This leads a version of Jensen's inequality for geometric integrals of matrix-valued integrable random variables.

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  1. On generalization of Williamson's theorem to real symmetric matrices

    math.FA 2024-08 unverdicted novelty 6.0

    Generalizes Williamson's theorem to real symmetric matrices allowing arbitrary real symplectic eigenvalues, with explicit constructions and perturbation bounds for the class EigSpSm(2n).