Endpoint Geodesies on the Set of Positive Definite Real Matrices

摘要

In this paper we study the endpoint geodesies problem on the differentiable manifold of real positive definite matrices. The objective is to connect two points given as initial data on that space by a unique geodesic. We first recall partially well-known facts about the differential geometry of this manifold. Then we consider further features, namely the property of being an extrinsic symmetric space together with associated Riemannian isometries. This paper is essentially self-contained and therefore accessible to a wide audience.