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A central problem in many areas (signal processing, algebraic statistics, complexity theory etc., see e.g., [4, 8, 21, 16]) is to understand the ranks and border ranks of 3-way tensors. Let A,B,C be complex vector spaces of dimensions a,b, c, and let p ∈ A⊗B⊗C. One would like to express p as a sum of decomposable tensors, just as one diagonalizes matrices… (More)

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