A 60-Addition, Rank-23 Scheme for Exact 3x3 Matrix Multiplication

TL;DR

This paper presents a new method that reduces the number of additions needed for exact 3x3 matrix multiplication from 61 or 62 to 60, setting a new record without changing the basis.

Contribution

It introduces a novel 60-addition scheme for exact 3x3 matrix multiplication, improving the previous best known additive complexity.

Findings

Achieved the lowest known additive complexity of 60 for 3x3 matrix multiplication.

No change of basis was required for this reduction.

Sets a new state-of-the-art in matrix multiplication complexity.

Abstract

We reduce the additive cost of general (non-commutative) 3x3 matrix multiplication from the previous records of 61 (Schwartz-Vaknin, 2023) and 62 (Martensson-Wagner, 2025) to 60 without a change of basis. To our knowledge, this represents a new state-of-the-art.