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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The border rank of the multiplication of $ 2\times 2$ matrices is seven


Author: J. M. Landsberg
Journal: J. Amer. Math. Soc. 19 (2006), 447-459
MSC (2000): Primary 68Q17
Published electronically: September 26, 2005
MathSciNet review: 2188132
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Abstract: We prove that the bilinear map corresponding to matrix multiplication of $ 2 \times 2$ matrices is not the limit of a sequence of bilinear maps that can be executed by performing six multiplications. This solves a longstanding problem dating back to Strassen's discovery in 1968 that the map could be executed by performing seven multiplications.


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Additional Information

J. M. Landsberg
Affiliation: Department of Mathematics, Texas A& M University, College Station, Texas 77843-3368
Email: jml@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-05-00506-0
PII: S 0894-0347(05)00506-0
Keywords: Border rank, complexity of matrix multiplication, secant varieties
Received by editor(s): August 23, 2004
Published electronically: September 26, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.