Moments for Left Elliptically Contoured Random Matrices

For a left elliptically contoured n × p random matrix Y LECn × p(μ, K, φ), the mth order moment E(⊗mY) is obtained in terms of μ, K, and φ. When K = B ⊗ C, LECn × p(μ, K, φ) is the conventional multivariate left elliptically contoured distribution MLEC(μ, A ⊗ Σ, φ), where A = B′B and Σ = C′C. Even if Y Nn × p(μ, ΣY), the formula given here is new in that μ need not be 0 and ΣY need not have the form A ⊗ Σ.