A 2n2 - log2(n)-1 Lower Bound for the Border Rank of Matrix Multiplication
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The Author(s) 2017. Let M(n) n2 n2n2 denote the matrix multiplication tensor for n n matrices. We use the border substitution method [2, 3, 6] combined with Koszul flattenings [8] to prove the border rank lower bound R(M(n,n,n)) 2n2 - log2(n)-1.