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arXiv · 2604.27645

An Exact 56-Addition, Rank-23 Scheme for General 3*3 Matrix Multiplication

Yinqi Sun
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Abstract

We present a rank-$23$ algorithm for general $3\times3$ matrix multiplication that uses $56$ additions/subtractions and $23$ multiplications, for a total of $79$ scalar operations in the standard bilinear straight-line model. This improves the recent sequence of $60$-, $59$-, and $58$-addition rank-$23$ schemes. The algorithm works over arbitrary associative, possibly noncommutative, coefficient rings. Its tensor coefficients are ternary, meaning that every coefficient lies in $\{-1,0,1\}$. Correctness is certified by the $729$ Brent equations over $\mathbb{Z}$, and the verifier also expands the straight-line program and performs additional finite-field and noncommutative implementation tests.

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Yinqi Sun. 2026-04-30. An Exact 56-Addition, Rank-23 Scheme for General 3*3 Matrix Multiplication. https://arxiv.org/abs/2604.27645

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