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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The border rank of the multiplication of $2\times 2$ matrices is seven
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by J. M. Landsberg PDF
J. Amer. Math. Soc. 19 (2006), 447-459 Request permission

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
  • MR Author ID: 288424
  • Email: jml@math.tamu.edu
  • Received by editor(s): August 23, 2004
  • Published electronically: September 26, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 19 (2006), 447-459
  • MSC (2000): Primary 68Q17
  • DOI: https://doi.org/10.1090/S0894-0347-05-00506-0
  • MathSciNet review: 2188132