since formula_102 This can be also seen as immediate consequence of the fact that formula_103. Note how this is equivalent to the observation that, if formula_104 is the set of eigenvectors of formula_69 corresponding to non-vanishing eigenvalues, then formula_106 is a set of orthogonal vectors, and formula_107 a (generally not complete) set of "orthonormal" vectors. This matches with the matrix formalism used above denoting with formula_89 the matrix whose columns are formula_104, with formula_90 the matrix whose columns are the eigenvectors of formula_69 which vanishing eigenvalue, and formula_112 the matrix whose columns are the vectors formula_107.