An orthogonal equivalence theorem for third order tensors

<p style='text-indent:20px;'>In 2011, Kilmer and Martin proposed tensor singular value decomposition (T-SVD) for third order tensors. Since then, T-SVD has applications in low rank approximation, recovery, multi-view clustering, feature extraction, sketching, etc. By going through the Discrete Fourier Transform (DFT), matrix SVD inverse DFT, a is mapped to an f-diagonal tensor. We call this Kilmer-Martin mapping. show that mapping of invariant if taking T-product with some orthogonal define values T-rank based upon its Thus, tubal rank, T-rank, T-singular are when it Some properties values, best one approximation discussed.</p>