English

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}
}