A determinant representation for the distribution of quadratic forms in complex normal vectors

Let the column vectors of X: M x 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 x 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\. (C) 2000 Academic Press.