Following the pattern that yields a generalization of Kruskal's criterion for the uniqueness of a decomposition in the symmetric case (reshaped Kruskal), we explore how properties of tensor products and Segre products can be used to extend Kruskal's criterion also in the setting of general tensors. Linear algebra and projective geometry are strongly interconnected in this research, and together they provide hints, and suggest conjectures, for new perspectives.
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