Symmetries of matrix multiplication algorithms. I

V. P. Burichenko

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arXiv · 1508.01110

Symmetries of matrix multiplication algorithms. I

V. P. Burichenko

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Abstract

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 $S_3\times Z_2$ and $S_4$ 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.

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V. P. Burichenko. 2015-08-05. Symmetries of matrix multiplication algorithms. I. https://arxiv.org/abs/1508.01110

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