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

• Received 22 January 2004

DOI:https://doi.org/10.1103/PhysRevE.69.065101