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arXiv · 1710.00494

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

Fumio Hiai·Yongdo Lim
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Abstract

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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Fumio Hiai, Yongdo Lim. 2017-10-02. Log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter. https://arxiv.org/abs/1710.00494

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