  In this paper, we study the approximate orthogonal diagonalization problem of
third order symmetric tensors. We define several classes of approximately
diagonal tensors, including the ones corresponding to the stationary points of
this problem. We study the relationships between these classes, and other
well-known objects, such as tensor Z-eigenvalue and Z-eigenvector. We also
prove results on convergence of the cyclic Jacobi (or Jacobi CoM2) algorithm.
