2018/04/12 by Jinmi Hwang, Hwang, Jinmi, Sejong Kim +1 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Inequalities and Applications #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1804.04323
openalex publication_date 2018/04/12 · openalex created_date 2018/04/24 · openalex updated_date 2026/07/28
As the least squares mean for the Riemannian trace metric on the cone of positive definite matrices, the Riemannian mean with its computational and theoretical approaches has been widely studied. Recently the new metric and the least squares mean on the cone of positive definite matrices, which are called the Wasserstein metric and the Wasserstein mean, respectively, have been introduced. In this paper, we explore some properties of Wasserstein mean such as determinantal inequality and find bounds for the Wasserstein mean. Using bounds for the Wasserstein mean, we verify that the Wasserstein mean is the multivariate Lie-Trotter mean.