A formula for the determinant of a matrix in terms of powers of traces is presented. Then, some expansions for powers of determinants of positive definite matrices in terms of zonal polynomials are derived. By making use of these, the associated elliptical families of matrix-variate...

A new series representation of the exact distribution of Hotelling's generalized T_{0}^{2}statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the noncentral distributions. Earlier results by...