The next step finds the principal values of the symmetric part of \mathbf{A}. Even though the eigenvalues of a real non-symmetric tensor might be complex, the eigenvalues of its symmetric part will always be real and therefore can be ordered from largest to smallest. The corresponding orthonormal principal basis directions can be assigned senses to ensure that the axial vector \mathbf{w} points within the first octant. With respect to that special basis, the components of \mathbf{A} are
