A 5/2n2-Lower Bound for the Multiplicative Complexity of n × n-Matrix Multiplication

  • Markus Bläser
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)


We prove a lower bound of 5/2n 2-3n for the multiplicative complexity of n × n-matrix multiplication over arbitrary fields. More general, we show that for any finite dimensional semisimple algebra A with unity, the multiplicative complexity of the multiplication in A is bounded from below by 5/2 dim A - 3(n 1 + ⋯ + n t) if the decomposition of A ≅= A1 x ... x At into simple algebras Aτ ≅ Dτ× contains only noncommutative factors, that is, the division algebra Dτ is noncommutative or nτ ≥ 2.


Matrix Multiplication Associative Algebra Division Algebra Multiplicative Complexity Semisimple Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Markus Bläser
    • 1
  1. 1.Institut für Theoretische InformatikMed. Universität zu LübeckLübeckGermany

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