The algorithmic complexity of linear algebras

  • A. Alder
  • V. Strassen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 122)


The complexity L(A) of a finite dimensional associative algebra A is the number of non-scalar multiplications/divisions of an optimal algorithm to compute the product of two elements of the algebra. We show
$$L(A) \geqslant 2 \cdot dimA - t,$$
where t is the number of maximal two-sided ideals of A.


Matrix Multiplication Left Ideal Division Algebra Linear Independence Semisimple Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • A. Alder
    • 1
  • V. Strassen
    • 1
  1. 1.University of ZürichSwitzerland

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