A $2n^2-log(n)-1$ lower bound for the border rank of matrix multiplication
Computational Complexity
2016-08-29 v1 Algebraic Geometry
Abstract
Let M_n denote the matrix multiplication tensor for nxn matrices. We use the border substitution method combined with Koszul flattenings to prove the border rank lower bound of 2n^2-log(n)-1 for M_n.
Keywords
Cite
@article{arxiv.1608.07486,
title = {A $2n^2-log(n)-1$ lower bound for the border rank of matrix multiplication},
author = {J. M. Landsberg and Mateusz Michałek},
journal= {arXiv preprint arXiv:1608.07486},
year = {2016}
}