  Using random matrix technique we determine an exact relation between the
eigenvalue spectrum of the covariance matrix and of its estimator. This
relation can be used in practice to compute eigenvalue invariants of the
covariance (correlation) matrix. Results can be applied in various problems
where one experimentally estimates correlations in a system with many degrees
of freedom, like in statistical physics, lattice measurements of field theory,
genetics, quantitative finance and other applications of multivariate
statistics.
