Riemannian metrics on positive definite matrices related to means

F. Hiai, D. Petz

The Riemannian metric on the manifold of positive definite matrices is defined by a kernel function $\varphi$ in the form $K_D^{\varphi }(H,K)={\sum }_{i,j}\varphi ({\lambda }_i,{\lambda }_j{)}^{-1}Tr{P}_{i}H{P}_{j}K$ when $\sum_iλ…