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Limits RegistryVolker Strassen showed in 1969 that two 2x2 matrices can be multiplied with 7 multiplications instead of 8, yielding the first sub-cubic matrix multiplication algorithm. In 1971 Shmuel Winograd (and independently Hopcroft and Kerr) proved that 7 multiplications are optimal for 2x2 matrices.
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Volker Strassen showed in 1969 that two 2x2 matrices can be multiplied with 7 multiplications instead of 8, yielding the first sub-cubic matrix multiplication algorithm. In 1971 Shmuel Winograd (and independently Hopcroft and Kerr) proved that 7 multiplications are optimal for 2x2 matrices.
Seven multiplications are necessary and sufficient to multiply two 2x2 matrices over a ring with noncommutative entries (bilinear rank of the 2x2 matrix multiplication tensor is 7).
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Limits Registry. LR-STRASSEN-2X2-OPTIMAL-MULTIPLICATIONS. Minimum multiplications for 2x2 matrix multiplication (proved optimal). 2026.