Consequences of the Moosbauer-Poole Algorithms

[Submitted on 9 May 2025]

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Abstract:Moosbauer and Poole have recently shown that the multiplication of two $5\times 5$ matrices requires no more than 93 multiplications in the (possibly non-commutative) coefficient ring, and that the multiplication of two $6\times 6$ matrices requires no more than 153 multiplications. Taking these multiplication schemes as starting points, we found improved matrix multiplication schemes for various rectangular matrix formats using a flip graph search.