  We discuss an application of the random matrix theory in the context of
estimating the bipartite entanglement of a quantum system. We discuss how the
Wishart ensemble (the earliest studied random matrix ensemble) appears in this
quantum problem. The eigenvalues of the reduced density matrix of one of the
subsystems have similar statistical properties as those of the Wishart
matrices, except that their {\em trace is constrained to be unity}. We focus
here on the smallest eigenvalue which serves as an important measure of
entanglement between the two subsystems. In the hard edge case (when the two
subsystems have equal sizes) one can fully characterize the probability
distribution of the minimum eigenvalue for real, complex and quaternion
matrices of all sizes. In particular, we discuss the important finite size
effect due to the {\em fixed trace constraint}.
