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 =\mid x -}\mathbf{x}\tilde{\mathbf{x}} is the least quares solution of\tilde \tilde{\mathbf{x}}.