Fourth-Order Properties of Normally Distributed Random Matrices

Abstract Three results are given involving a normally distributed matrix X , namely (1) the expectation of X ′ AXCX ′ BX , (2) the covariance of vec X ′ AX and vec X ′ BX , and (3) the expectation of X ⊗ X ⊗ X ⊗ X .