Geometries on the cone of positive-definite matrices derived from the power potential and their relation to the power means

Nadia Chouaieb, Bruno Iannazzo, Maher Moakher

We study a Riemannian metric on the cone of symmetric positive-definite matrices obtained from the Hessian of the power potential function $(1-\det (X{)}^{\beta })/\beta$. We give explicit expre…