ON THE MOMENTS OF A KIND OF ELLIPTICAL MATRIX DISTRIBUTIONS

Let X be an m×n random matrix, n≥m and S=XX’. If Γ∈O_m,\Gamma X \stackreld= X then for any integer k we get E（S^k）=c^kI_m cov（vec S^k）=α_kI_m²+β_kK_m²+γ_kQ_m² Where α_k,β_k,γ_kandc_k are some constants, \beginaligned K_m 2 & =\sum_i j=1^m H_i \otimes H_i j^\prime ; \\ Q_m^2 & =\sum_i j=1^m H_i j \otimes H_i j ;\endaligned here H_ij denotes the m×m matrix with h_ij=1 and all other elements zero and \otimes denotes Kroncker producte. Some special α_k,β_k,γ_kandc_k are found.