On the 2*2 matrix multiplication

In SIAM J. Comput., vol.5, p.187-203 (1976), R.L. Probert proved that 15 additive operations are necessary and sufficient to multiply two 2*2 matrices over the binary field by a bilinear algorithm using seven non-scalar multiplications. The author proves this result for arbitrary field. The algorithm of Winograd is used to classify all such algorithms (S. Winograd, 1971).<
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