# Symmetries of matrix multiplication algorithms. I

arXiv: https://arxiv.org/abs/1508.01110 · HTML: https://mlsanity.com/paper/1508.01110/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2015.

## Built on by (most cited first, 1 of 1)

- [Fast Matrix Multiplication in fp8: Certified Coefficient Optimization and Measured Error](https://mlsanity.com/paper/2609.26077/) (2026)

## Abstract (arXiv)

In this work the algorithms of fast multiplication of matrices are considered. To any algorithm there associated a certain group of automorphisms. These automorphism groups are found for some well-known algorithms, including algorithms of Hopcroft, Laderman, and Pan. The automorphism group is isomorphic to S3× Z2 and S4 for Hopcroft anf Laderman algorithms, respectively. The studying of symmetry of algorithms may be a fruitful idea for finding fast algorithms, by an analogy with well-known optimization problems for codes, lattices, and graphs. em Keywords: Strassen algorithm, symmetry, fast matrix multiplication.