A Brief Derivation of Necessary and Sufficient Conditions for a Family of Matrix Quadratic Forms to Have Mutually Independent Non-Central Wishart Distributions

We provide a new, concise derivation of necessary and sufficient conditions for a real matrix-normally distributed matrix X and we characterize the general matrix-normal covariance structure such that, given the symmetric positive-semidefinite matrices A i , i = 1,2,..., m , the matrix quadratic forms X^'A_iX are distributed as independent noncentral Wishart matrices.