it follows from the definition of a pure tensor that formula_78 if and only if there exist formula_79 such that formula_80 and formula_81 for all "k". for this reason, the parameters formula_82 of a rank-1 tensor formula_69 are called identifiable or essentially unique. a rank-formula_6 tensor formula_85 is called identifiable if every of its tensor rank decompositions is the sum of the same set of formula_6 distinct tensors formula_87 where the formula_88's are of rank 1. an identifiable rank-formula_6 thus has only one essentially unique decomposition formula_90and all formula_91 tensor rank decompositions of formula_69 can be obtained by permuting the order of the summands. observe that in a tensor rank decomposition all the formula_88's are distinct, for otherwise the rank of formula_69 would be at most formula_95.