Before revision:  To detect the correlations in the reduced matrix, which we still call A, we consider a perturbation }\tilde =\mid x -}\mathbf{x}\tilde{\mathbf{x}} \tilde \tilde{\mathbf{x}}.
After revision:  To detect the correlations in the reduced matrix, which we still call A, we consider a perturbation }\tilde A of A. We prove that correlations are encoded in \Delta\mathbf{x=\mid x -}\mathbf{x}\tilde{\mathbf{x}} \tilde \tilde{\mathbf{x}}.