The alternative Heinz means of matrices

Abstract

In this article, we introduce alternative Heinz means (Formula presented.) of positive definite matrices A and B. This family of symmetric means interpolates between the spectral geometric and Wassserstein means. We prove that it satisfies several desirable properties of means, including near-order monotonicity. Moreover, we obtain several bounds for (Formula presented.) in terms of other means. Furthermore, we derive connections to the spectral Heinz means.