Refined methods for the identifiability of tensors

Abstract

We prove that the general tensor of size 2n and rank k has a unique decomposition as the sum of decomposable tensors if (Formula presented.) (the constant 1 being the optimal value). Similarly, the general tensor of size 3n and rank k has a unique decomposition as the sum of decomposable tensors if (Formula presented.) (the constant 1 being the optimal value). Some results of this flavor are obtained for tensors of any size, but the explicit bounds obtained are weaker.