On the distributions of the latent roots and traces of certain random matrices

It is shown that differential equations given by the author may be used recursively to construct certain multivariate null distributions in reduced form. These include the distributions of individual latent roots of B = S₁(S₁ + S₂)⁻¹, and distributions of Tr B and Tr S₁S₂⁻¹, for small numbers of variates.