on complex random variables

In this paper,it is shown that a complex multivariate random variable z = (z 1,z 2,...,z p)',is a complex multivariate normal random variable of dimensionality p if and only if all nondegenerate complex linear combinations of z have a complex univariate normal distribution. the characteristic function of z has been derived,and simpler forms of some theorems have been given using this characterization theorem without assuming that the variance-covariance matrix of the vector z is hermitian positive definite. marginal distributions of z have been given. in addition,a complex multivariate t-distribution has been defined and the density derived. a characterization of the complex multivariate t-distribution is given. a few possible uses of this distribution have been suggested.