The Bures-Wasserstein distance on positive definite matrices

Tuesday, July 11, 2017
Ora Inizio: 
Ora Fine: 
Rajendra Bhatia
Indian Statistical Institute, Delhi

We will discuss an interesting metric on the space of positive definite matrices, called the Bures distance in the quantum information literature and the Wasserstein metric in optimal transport. This has connections with Riemannian geometry, statistics, QIT and optimal transport. We will explain these connections. The two-variable and several-variable mean with respect to this metric will be described. Our perspective from matrix analysis leads to simpler proofs and suggests new problems.