A non-commutative algorithm for multiplying a 3×4 matrix by a 4×7 matrix using 63 non-complex multiplications
Résumé
The number of scalar multiplications required to multiply a $3\times4$ matrix by a $4\times7$ matrix was reduced from 66 in [11] to 63 in [9] by an algorithm over complex numbers. We propose an algorithm in 63 multiplications with only rational coefficients, hence removing the requirement that the base field for the arithmetic operations contains a square root of -1, while it still needs to contain an inverse of 2. It was derived from the latter one, under the action of an isotropy which happen to project the algorithm on the field of rational numbers. We also produce a straight line program of this algorithm.
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