  We compute exact asymptotic of the statistical density of random matrices
belonging to invariant random matrices ensemble (RMT) orthogonal, unitary and
symplectic ensembles, where all its eigenvalues lie within the interval
$[\sigma, +\infty[$ or $]-\infty,\tau]$ or $[\sigma,\tau]$. It is found that
the density of eigenvalues generically exhibits an inverse square-root
singularity at the location of the barriers. These results generalized the case
of Gaussian random matrices ensemble studied by Dean-Majumdar.
