The border rank of the multiplication of $2 imes 2$ matrices is seven Academic Article uri icon


  • 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.

published proceedings

  • Journal of the American Mathematical Society

altmetric score

  • 10.536

author list (cited authors)

  • Landsberg, J. M.

citation count

  • 34

complete list of authors

  • Landsberg, JM

publication date

  • September 2005