ST-SVD factorization and s-diagonal tensors

A third order real tensor is mapped to a special f-diagonal by going through Discrete Fourier Transform (DFT), standard matrix SVD and inverse DFT. We call such an s-diagonal tensor. An if only it itself in the above process. The space partitioned orthogonal equivalence classes. Each class has unique Two tensors are equal they orthogonally equivalent. Third have same tubal rank T-singular values. Four meaningful necessary conditions for presented. Then we present set of sufficient tensors. Such involve complex number. In cases that dimension mode considered $2, 3$ $4$, direct which do not