Non-existence of a short algorithm for multiplication of 3×3 matrices whose group is S4×S3, II
Abstract
It is proved that there is no algorithm for multiplication of $3\times3$ matrices of multiplicative length $\leq23$ that is invariant under a certain group isomorphic to $S_4\times S_3$. The proof uses description of the orbits of this group on decomposable tensors in the tensor cube $(M_3({\mathbb C}))^{\otimes}$ 3 which was obtained earlier.
About the Author
V. P. Burichenko
Institute of Mathematics of the National Academy of Sciences of Belarus
Russian Federation
Russian Federation
References
1. Burichenko V. P. Non-existence of a short algorithm for multiplication of 3×3 matrices with group S<sub>4</sub>×S<sub>3</sub> // Тр. Ин-та математики [Proceedings of the Institute of mathematics]. 2022. Т. 30, № 1–2. С. 99–116.
2. Burichenko V. P. Symmetries of matrix multiplication algorithms. I // arXiv preprint, arXiv: 1508.01110,2015.arXiv.org
3. Burichenko V. P. The isotropy group of the matrix multiplication tensor // Тр. Ин-та математики [Proceedings of the Institute of mathematics]. 2016. Т. 24, № 2. С. 106–118.
4. Brent R. P. Algorithms for matrix multiplication // Technical report 70-157, Stanford university, Computer Science Department, 1970. Available at: http://maths-people.anu.edu.au/brent/pub/pub002.html.
Review
For citations:
Burichenko V.P. Non-existence of a short algorithm for multiplication of 3×3 matrices whose group is S4×S3, II. Trudy Instituta matematiki. 2023;31(1):101-111.
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