Quasi-Wasserstein Means of Matrices

Abstract

In this article we introduce and study properties of a new family of two-variable means that interpolate between the weighted spectral geometric and Wasserstein means of positive definite matrices. This new family of means are called quasi-Wasserstein means. We show that they behave with respect to the near order, analogously to the Lim-Palfia’s power means in the Loewner order.