  Using a character expansion method, we calculate exactly the eigenvalue
density of random matrices of the form M^\dagger M where M is a complex matrix
drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A
and B positive definite (square) matrices of arbitrary dimensions. Such
so-called ``correlated Wishart matrices'' occur in many fields ranging from
information theory to multivariate analysis.
