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A 2n<sup>2</sup>-log<sub>2</sub>(n)-1 lower bound for the border rank of matrix multiplication

A 2n2-log2(n)-1 lower bound for the border rank of matrix multiplication

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LANDSBERG, Joseph M., Mateusz MICHALEK, 2018. A 2n2-log2(n)-1 lower bound for the border rank of matrix multiplication. In: International Mathematics Research Notices. Oxford University Press (OUP). 2018(15), pp. 4722-4733. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnx025

@article{Landsberg2018lower-53233, title={A 2n2-log2(n)-1 lower bound for the border rank of matrix multiplication}, year={2018}, doi={10.1093/imrn/rnx025}, number={15}, volume={2018}, issn={1073-7928}, journal={International Mathematics Research Notices}, pages={4722--4733}, author={Landsberg, Joseph M. and Michalek, Mateusz} }

terms-of-use 2018 Michalek, Mateusz A 2n<sup>2</sup>-log<sub>2</sub>(n)-1 lower bound for the border rank of matrix multiplication Michalek, Mateusz 2021-03-23T09:44:04Z Landsberg, Joseph M. 2021-03-23T09:44:04Z Landsberg, Joseph M. Let M<sub>⟨n⟩</sub> ∈ C<sup>n2</sup>⊗C<sup>n2</sup>⊗C<sup>n2</sup> 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<sub>⟨n,n,n⟩</sub>)≥2n<sup>2</sup>−⌈log<sub>2</sub>(n)⌉−1⁠. eng

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