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

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

2004-07-13

arxiv.org/abs/math/0407224v3

J. Amer. Math. Soc. 19 (2006), no. 2, 447--459

Mathematics

Algebraic Geometry

version published in JAMS plus expanded erratum

Scientific paper

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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