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On Generic Nonexistence of the Schmidt--Eckart--Young Decomposition for Complex Tensors
The Schmidt--Eckart--Young theorem for matrices states that the optimal rank-$r$ approximation of a matrix is obtained by retaining the first $r$ terms from the singular value decomposition of that matrix. This paper considers a generalization of this optimal truncation property to the rank decomposition (Candecomp/Parafac) of tensors and establishes a …