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arXiv · 2609.32388

A 51-Addition Alternative-Basis Kernel for Rank-23 $3\times3$ Matrix Multiplication

Joshua Stapleton·Andrew Perminov
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Abstract

We give a rank-23 algorithm for $3\times3$ matrix multiplication using 51 additions and subtractions in alternative bases. The input and output conversions require five further additions, giving 56 additions in ordinary coordinates. The construction combines linear-program reduction with a search over sparse basis changes, and the resulting programs are distributed as a machine-checkable certificate. We verify correctness by exact coefficient expansion and distinguish the kernel cost from the cost of a complete multiplication.

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Joshua Stapleton, Andrew Perminov. 2026-09-26. A 51-Addition Alternative-Basis Kernel for Rank-23 $3\times3$ Matrix Multiplication. https://arxiv.org/abs/2609.32388

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