By means of the transformations the symmetric tensor "nab" can be brought to diagonal form with eigenvalues "n"1, "n"2, "n"3. Equation shows that the vector "ab" (if it exists) lies along one of the principal directions of the tensor "nab", the one corresponding to the eigenvalue zero. Without loss of generality one can therefore set "ab" = ("a", 0, 0). Then reduces to "an"1 = 0, i.e. one of the quantities "a" or "n"1 must be zero. The Jacobi identities take the form: