On the dispersion matrix of a matrix quadratic form connected with the noncentral Wishart distribution

Abstract

Recently Magnus and Neudecker [3] derived the dispersion matrix of vec X′ X, when X′ is a p × n random matrix ( n > p) and vec X′ has the distribution N np(vec M′, I n ⊗ V) . This note is concerned with the matrix quadratic form X′ AX, where X′ is a defined above and A is a nonrandom (not necessarily symmetric) matrix. The dispersion matrix of vec X′ AX is then derived by applying results of Magnus and Neudecker [3] and Neudecker and Wansbeek [4]. This generalizes an earlier result of Giguère and Styan [2] which assumes a symmetric A.