The border rank of the multiplication of 2x2 matrices is seven Academic Article

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.

authors

• Landsberg, Joseph

published proceedings

• JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

altmetric score

• 13.536

author list (cited authors)

• Landsberg, J. M.

citation count

• 38

complete list of authors

• Landsberg, JM

publication date

• September 2006

publisher

• American Mathematical Society (AMS)  Publisher

published in

• Journal of the American Mathematical Society  Journal

keywords

• Border Rank
• Complexity Of Matrix Multiplication
• Secant Varieties

Digital Object Identifier (DOI)

• 10.1090/S0894-0347-05-00506-0

start page

• 447

end page

• 459

volume

• 19

issue

• 2