Spherical Matrix Distributions and Cauchy Quotients
It is shown that matrix quotients of submatrices of a spherical matrix are distributed as matrix Cauchy. This generalizes known results for scalar ratios of independent normal variates. The derivations are simple and make use of the theory of invariant measures on manifolds.
Phillips, Peter C.B., "Spherical Matrix Distributions and Cauchy Quotients" (1987). Cowles Foundation Discussion Papers. 1066.