What question did this study set out to answer?

The aim is to establish a lower bound for the border rank of the matrix multiplication tensor.

January 30, 2017Open Access

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

JLJ. M. LandsbergTexas A&M University MMMateusz MichałekJagiellonian University

Key Points

The aim is to establish a lower bound for the border rank of the matrix multiplication tensor.
Employed the border substitution method for analysis.
Utilized Koszul flattenings to derive the lower bound.
The established lower bound is $2n^2 - \log_2(n) - 1$.

Abstract

Let M n C n 2 C n 2 C n 2 denote the matrix multiplication tensor for n n matrices. We use the border substitution method 2, 3, 6 combined with Koszul flattenings

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