Moments for Left Elliptically Contoured Random Matrices

For a left elliptically contoured n - p random matrix Y LECn - p([mu], K, [phi]), the mth order moment E([circle times operator]mY) is obtained in terms of [mu], K, and [phi]. When K = B [circle times operator] C, LECn - p([mu], K, [phi]) is the conventional multivariate left elliptically contoured distribution MLEC([mu], A [circle times operator] [Sigma], [phi]), where A = B'B and [Sigma] = C'C. Even if Y Nn - p([mu], [Sigma]Y), the formula given here is new in that [mu] need not be 0 and [Sigma]Y need not have the form A [circle times operator] [Sigma].