On the Nuclear Norm and the Singular Value Decomposition of Tensors

Finding the rank of a tensor is a problem that has many applications. unfortunately, it is often very difficult to determine the rank of a given tensor. inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of the rank of a tensor. we determine the nuclear norm of various tensors of interest. along the way, we also do a systematic study various measures of orthogonality in tensor product spaces and we give a new generalization of the singular value decomposition to higher-order tensors.