Doubly Autoparallel Structure on Positive Definite Matrices and Its Applications

Abstract

In a statistical manifold, we can naturally define submanifolds that are simultaneously autoparallel with respect to both the primal and the dual affine connections of the statistical manifold. We call them doubly autoparallel submanifolds. The aim of this paper is to mainly introduce doubly autoparallelism on positive definite matrices in linear algebraic way and show its applicability to two related topics.