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