Some generalized commutation matrices are defined and used to establish relationships between @-products and Kronecker products. These are applied to obtain expectations of @-products of random vectors and matrices.
RESUMEOn dCfinit des gkntralisations de matrices de "commutation" et on les utilise pour Ctablir des relations entre des @-produits et des produits de Kronecker. A partir de ces relations, on obtient des espkrances de @-produit, de vecteurs et matrices alkatoires. Vol. 17, No. 1 Neudecker, H., and Wansbeek, T. (1983). Some results on commutation matrices with statistical applications. Singh, R.P. (1972). Some generalizations in matrix differentiation with applications in multivariate analysis. Tracy, D.S., and Dwyer, P.S. (1969). Multivariate maxima and minima with matrix derivatives. J . Amer. Tracy, D.S., and Jinadasa, K.G. (1985). On generalized least squares estimation in inter-battery factor analysis. Tracy, D.S., and Singh, R.P. (1972). A new matrix product and its applications in partitioned matrix differen-Canad. J . Statist., 11, 221-231. Ph.D. Dissertation, University of Windsor. Statist. Assoc., 64, 1576-1594. Pakistan J . Statist., 1, 79-90. tiation. Statist. Neerfand., 26, 143-157.