On the dispersion matrix of a matrix quadratic form connected with the noncentral Wishart distribution
Recently \textit{J. R. Magnus} and the author [Ann. Stat. 7, 381-394 (1979; Zbl 0414.62040)] derived the dispersion matrix of vec X'X, when X' is a \(p\times n\) random matrix \((n>p)\) and vec X' has the distribution \({\mathcal N}_{np}(vec M',I_ n\otimes V)\). This note is concerned with the matrix quadratic form X'AX, where X' is as 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 the author (op. cit.) and the author and \textit{T. Wansbeek} [Can. J. Stat. 11, 221- 231 (1983; Zbl 0538.15011)]. This generalizes an earlier result of \textit{M. A. Giguère} and \textit{G. P. H. Styan} [Information theory, statistical decision functions, random processes; Trans. 7th Prague Conf., Vol. B, Prague 1974, 129-139 (1978; Zbl 0406.62033)] which assumes a symmetric A.
scientific article; zbMATH DE number 3988491