# Description of fast matrix multiplication algorithm: ⟨3×3×3:23⟩

# Algorithm type

$4{X}^{2}{Y}^{2}{Z}^{2}+2{X}^{3}YZ+2X{Y}^{3}Z+2XY{Z}^{3}+13XYZ$# Algorithm definition

The algorithm ⟨3×3×3:23⟩ is taken from:

Julian David Laderman. A noncommutative algorithm for multiplying 3×3 matrices using 23 multiplications. Bulletin of the American Mathematical Society, 82(1):126--128, January 1976. [DOI] |

# Algorithm description

# Algorithm symmetries

The following group of 24 isotropies acts as a permutation group on algorithm tensor representation:These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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