  We investigate the problem of estimating a given real symmetric signal matrix
$\textbf{C}$ from a noisy observation matrix $\textbf{M}$ in the limit of large
dimension. We consider the case where the noisy measurement $\textbf{M}$ comes
either from an arbitrary additive or multiplicative rotational invariant
perturbation. We establish, using the Replica method, the asymptotic global law
estimate for three general classes of noisy matrices, significantly extending
previously obtained results. We give exact results concerning the asymptotic
deviations (called overlaps) of the perturbed eigenvectors away from the true
ones, and we explain how to use these overlaps to "clean" the noisy eigenvalues
of $\textbf{M}$. We provide some numerical checks for the different estimators
proposed in this paper and we also make the connection with some well known
results of Bayesian statistics.
