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

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.

version published in JAMS plus expanded erratum

Cited by in corpus (6)

• Induction for secant varieties of Segre varieties
• Generation and syzygies of the first secant variety
• The border support rank of two-by-two matrix multiplication is seven
• Equations for lower bounds on border rank
• Secant varieties of Segre-Veronese varieties P^m x P^n embedded by O(1,2)
• Arithmetic properties of the first secant variety to a projective variety