The border rank of the multiplication of 2 × 2 matrices is seven
by
J. M. Landsberg
| Venue: | J. Amer. Math. Soc |
| Citations: | 5 - 1 self |
BibTeX
@ARTICLE{Landsberg_theborder,
author = {J. M. Landsberg},
title = {The border rank of the multiplication of 2 × 2 matrices is seven},
journal = {J. Amer. Math. Soc},
year = {},
volume = {19},
pages = {447--459}
}
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Abstract
One of the leading problems of algebraic complexity theory is matrix multiplication. The naïve multiplication of two n × n matrices uses n 3 multiplications. In 1969, Strassen [20] presented an explicit algorithm for multiplying 2 × 2 matrices using seven multiplications. In the opposite direction, Hopcroft and Kerr [12] and
