Eigenvalue density of correlated complex random Wishart matrices

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^M where M is a complex matrix drawn from a normalized distribution P(M)~exp(-TrAMBM^) 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.