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Several conjectures and partial proofs have been formulated on the(non)existence of a best low-rank approximation of real-valued IxJx2 arrays. Weanalyze this problem using the Generalized Schur Decomposition and prove(non)existence of a best rank-R approximation for generic IxJx2 arrays, for allvalues of I,J,R. Moreover, for cases where a best rank-R approximation existson a set of positive volume only, we provide easy-to-check necessary andsufficient conditions for the existence of a best rank-R approximation.

On the (non)existence of best low-rank approximations of generic IxJx2 arrays