Degeneracy in Candecomp/Parafac explained for p × p × 2 arrays of rank p + 1 or higher

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Tensor decompositions, alternating least squares and other tales (2009, background): “2 ) is nothing else but Kruskal’s polynomial mentioned in References[16,18,19],whichitselfisduetoCayley[40].”
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem (2006, unknown): “[49, 51, 62, 67, 68]) but we prefer to avoid this term since it is inconsistent (and often at odds) with common usage in Mathematics.”
Tensor Decompositions and Applications (2009, background): “Stegeman [202] considers the case of I × I × 2 arrays and proves that any tensor with rank R = I + 1 does not have a best rank-I approximation.”
Subtracting a best rank-1 approximation may increase tensor rank (2009, background): “Stegeman [23] showed that any sequence of rank-2 approximations y(n) for which II X - y(n) 112 con verges to the infimum of 1, features diverging components.”
On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode (2009, background): “Lundy [12], Stegeman [ 17 , 19, 18] and Krijnen, Dijkstra and Stegeman [9].”