A Determinant Representation for the Distribution of Quadratic Forms in Complex Normal Vectors

Let the column vectors of X:: M-N, M<N, be distributed as independent complex normal vectors with the same covariance matrix [Sigma]. Then the usual quadratic form in the complex normal vectors is denoted by Z=XLXH where L: N-N is a positive definite hermitian matrix. This paper deals with a representation for the density function of Z in terms of a ratio of determinants. This representation also yields a compact form for the distribution of the generalized variance Z.