Strassen's algorithm via orbit flip graphs

Christian Ikenmeyer; Jakob Moosbauer

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arXiv · 2503.05467

Strassen's algorithm via orbit flip graphs

Christian Ikenmeyer·Jakob Moosbauer

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Abstract

We give a short proof for Strassen's result that the rank of the 2 by 2 matrix multiplication tensor is at most 7. The proof requires no calculations and also no pattern matching or other type of nontrivial verification, and is based solely on properties of a specific order 6 group action. Our proof is based on the recent combination of flip graph algorithms and symmetries.

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Christian Ikenmeyer, Jakob Moosbauer. 2025-03-07. Strassen's algorithm via orbit flip graphs. https://arxiv.org/abs/2503.05467

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