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Given a multivariate complex centered Gaussian vectorZ = (  Z 1  , ⋯ ,  Z p  )with non-singular covariance matrix    Σ   , we derive sufficient conditions on the nullity of the complex moments and we give a closed-form expression for the non-null complex moments. We present conditions for the factorisation of the complex moments. Computational consequences of these results are discussed.

Computing the Moments of the Complex Gaussian: Full and Sparse Covariance Matrix