A Normal Form for Matrix Multiplication Schemes

Manuel Kauers; Jakob Moosbauer

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arXiv · 2206.00550

A Normal Form for Matrix Multiplication Schemes

Manuel Kauers·Jakob Moosbauer

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Abstract

Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for a large number of schemes a pairwise equivalence check becomes cumbersome. In this paper we propose an algorithm to compute a normal form of matrix multiplication schemes. This allows us to decide pairwise equivalence of a larger number of schemes efficiently.

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Manuel Kauers, Jakob Moosbauer. 2022-06-01. A Normal Form for Matrix Multiplication Schemes. https://arxiv.org/abs/2206.00550

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