  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.
