Title: Averaging of Positive Definite Matrices

Abstract:

In many problems the data sets are points on a manifold (like a sphere). An average of these has again to be a point on that manifold. In many problems (statistics, image processing, quantum information, optimal transport, …..) the data are positive definite matrices. Appropriate notions of an average that have certain theoretical properties and are useful in applications have been developed. In this talk we will discuss these.(Everyone would be able to get some idea of the problems. It would be helpful if you know some basic things about positive definite matrices.)