首页|Geometries on the cone of positive-definite matrices derived from the power potential and their relation to the power means
Geometries on the cone of positive-definite matrices derived from the power potential and their relation to the power means
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NSTL
Elsevier
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 expressions for the geodesics and distance function, under suitable conditions. In the scalar case, the geodesic between two positive numbers coincides with a weighted power mean, while for matrices of size at least two it yields a notion of weighted power mean different from the ones given in the literature. As beta tends to zero, the power potential converges to the logarithmic potential, that yields a well-known metric associated with the matrix geometric mean; we show that the geodesic and the distance associated with the power potential converge to the weighted matrix geometric mean and the distance associated with the logarithmic potential, respectively. (c) 2021 Elsevier Inc. All rights reserved.
NSTL
Elsevier
