Inequalities for the Wasserstein mean of positive definite matrices

2018/03/09 by Bhatia, Rajendra, Jain, Tanvi, Lim, Yongdo · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1803.03357

Abstract

We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.

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• On the Wasserstein barycenter of positive definite operators
• Tight bounds of norms of Wasserstein metric matrix

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