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The border rank of the multiplication of two by two matrices is seven

J. M. Landsberg
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Abstract

I show that 2x2 matrices cannot be approximately multiplied using less than seven multiplications. In other words I show that the matrix multiplication operator is not in the sixth secant variety of the Segre produt of three $P^3$'s.

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J. M. Landsberg. 2004-07-13. The border rank of the multiplication of two by two matrices is seven. https://arxiv.org/abs/math/0407224

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