  Quantum entanglement plays a crucial role in quantum information, quantum
teleportation and quantum computation. The information about the entanglement
content between subsystems of the composite system is encoded in the Schmidt
eigenvalues. We derive here closed expressions for the spectral density of
Schmidt eigenvalues for all three invariant classes of random matrix ensembles.
We also obtain exact results for average von Neumann entropy. We find that
maximum average entanglement is achieved if the system belongs to the
symplectic invariant class.
