A non-commutative algorithm for multiplying (7 $\times$ 7) matrices using 250 multiplications

TL;DR

This paper introduces new non-commutative algorithms for multiplying 7x7 and 9x9 matrices with fewer multiplications than traditional methods, using a divide-and-conquer approach.

Contribution

It presents novel non-commutative algorithms for matrix multiplication that reduce the number of multiplications needed for 7x7 and 9x9 matrices.

Findings

7x7 matrix multiplication with 250 multiplications

9x9 matrix multiplication with 520 multiplications

Algorithms use divide-and-conquer technique

Abstract

We present a non-commutative algorithm for multiplying (7x7) matrices using 250 multiplications and a non-commutative algorithm for multiplying (9x9) matrices using 520 multiplications. These algorithms are obtained using the same divide-and-conquer technique.