Technical Report CS0574

Title: On the 2x2 Matrix Multiplication
Authors: Nader H. Bshouty
Abstract: In [SIAM J. Comput, June 1976] Probert proved that 15 additive operations are necessary and sufficient to multiply two 2 x 2 matrices over the binary field by a bilinear algorithms using 7 non-scalar multiplications. We prove this result for arbitrary field. We also use the algorithm of Winograd to classify all such algorithms.
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