Inequalities for the Wasserstein mean of positive definite matrices
Rajendra Bhatia, Tanvi Jain, and Yongdo Lim
TL;DR
This paper establishes majorization inequalities for various means of positive definite matrices, including the Cartan, log Euclidean, Wasserstein, and power means, advancing the understanding of their relationships.
Contribution
The paper introduces new majorization inequalities for multiple matrix means, providing a unified framework for comparing these different types of means.
Findings
Majorization inequalities for the Cartan mean
Majorization inequalities for the log Euclidean mean
Majorization inequalities for the Wasserstein mean
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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