Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures Original Research Article

Let X be distributed as matrix normal with mean M and covariance matrix Wcircle times operatorV, where W and V are nonnegative definite (nnd) matrices. In this paper we present a simple version of the Cochranʹs theorem for matrix quadratic forms in X. The theorem is used to characterize the class of nnd matrices W such that the matrix quadratic forms that occur in multivariate analysis of variance are independent and Wishart except for a scale factor.