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The counterpart of the [[Kirchhoff matrix]] Γ of the GNM is simply (1/γ) Η in the ANM. Its decomposition yields 3N - 6 non-zero [[eigenvalues]], and 3N - 6 eigenvectors that reflect the respective frequencies and shapes of the individual modes. The inverse of Η, which holds the desired information about fluctuations is composed of N x N super-elements, each of which scales with the 3 x 3 matrix of correlations between the components of pairs of fluctuation vectors. The Hessian, however is not invertible, as its rank is 3N-6 (6 variables responsible to a rigid body motion). To obtain a pseudo inverse, a solution to the eigenvalue problem is obtained:<br />
<math>H =
The pseudo-inverse is composed of the 3N-6 eigenvectors and their respective non-zero eigen values. Where λi are the eigenvalues of H sorted by their size from small to large and Ui the corresponding eigenvectors. The eigenvectors (the columns of the matrix U) describe the vibrational direction and the relative amplitude in the different modes. <br />
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