We prove that the bilinear map corresponding to matrix multiplication of 2 × 2 2 × 2 matrices is not the limit of a sequence of bilinear maps that can be executed by performing six multiplications. This solves a longstanding problem dating back to Strassen’s discovery in 1968 that the map could be executed by performing seven multiplications.
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J. M. Landsberg (2005) studied this question.
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