Recently, the tensor singular value decomposition (t-SVD) based on t-product operation of third order tensors has draw intensive scholarly interest. Lately, a set of sufficient and necessary conditions were proposed to characterize the resulting f-diagonal tensor of the t-SVD procedure. Those special f-diagonal tensors are called s-diagonal tensors. In this paper, we eliminate the complex numbers involved in the previous conditions and present a new characterization in real matrix multiplication form. In addition, we find a way to construct s-diagonal tensors with some nonnegative vectors. Finally, some specific checking matrices are presented for reference.
展开▼
