contrary to the case of matrices, the rank of a tensor is presently not understood well. it is known that the problem of computing the rank of a tensor is np-hard. the only notable well-understood case consists of tensors in formula_15, whose rank can be obtained from the kronecker–weierstrass normal form of the linear matrix pencil that the tensor represents. a simple polynomial-time algorithm exists for certifying that a tensor is of rank 1, namely the higher-order singular value decomposition.