Title: Riemannian Gaussian distributions on the space of positive-definite quaternion matrices,
Abstract: Recently, Riemannian Gaussian distributions were defined on spaces of
positive-definite real and complex matrices. The present paper extends this
definition to the space of positive-definite quaternion matrices. In order to
do so, it develops the Riemannian geometry of the space of positive-definite
quaternion matrices, which is shown to be a Riemannian symmetric space of
non-positive curvature. The paper gives original formulae for the Riemannian
metric of this space, its geodesics, and distance function. Then, it develops
the theory of Riemannian Gaussian distributions, including the exact expression
of their probability density, their sampling algorithm and statistical
inference.