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

DOI10.1016/j.laa.2018.04.029zbMath1391.15065arXiv1710.00494OpenAlexW2963123155WikidataQ129883426 ScholiaQ129883426MaRDI QIDQ1642004

Yongdo Lim, Fumio Hiai

Publication date: 20 June 2018

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.00494

zbMATH Keywords

probability measurepositive definite matrixCartan barycenterRiemannian trace metriclog-majorizationsymplectic eigenvalue

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Positive linear operators and order-bounded operators (47B65) Convex sets and cones of operators (47L07) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Cites Work

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• Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices
• The Symmetry Group of Gaussian States in $${L}^{2}({\mathbb{R}}^{n})$$
• Matrix Analysis: Matrix Monotone Functions, Matrix Means, and Majorization
• On symplectic eigenvalues of positive definite matrices
• Contractive barycentric map

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