Strassen's algorithm via orbit flip graphs

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-07
Primary Topic
Tensor decomposition and applications
Type
article
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article

Strassen's algorithm via orbit flip graphs

ArXiv.org
Tensor decomposition and applications
article

Strassen's algorithm via orbit flip graphs

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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.

ArXiv.org
Openalex Percentile: Top 53%
Tensor decomposition and applications
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Strassen's algorithm via orbit flip graphs · ArXiv.org (2025) | TGRS Research Map | TGRS