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Some computational problems in linear algebra as hard as matrix multiplication

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Abstract

We define the complexity of a computational problem given by a relation using the model of computation trees together with the Ostrowski complexity measure. Natural examples from linear algebra are:

  • KER n : Compute a basis of the kernel for a givenn×n-matrix,

  • OGB n : Find an invertible matrix that transforms a given symmetricn×n-matrix (quadratic form) into diagonal form,

  • SPR n : Find a sparse representation of a givenn×n-matrix.

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Authors and Affiliations

  1. Institut für Informatik, Universität Bonn, D-5300, Bonn 1

    Peter Bürgisser & Marek Karpinski

  2. International Computer Science Institute, 94704, Berkeley, CA

    Marek Karpinski

  3. Fachbereich Mathematik, Universität Tübingen, D-7400, Tübingen

    Thomas Lickteig

Authors
  1. Peter Bürgisser
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  2. Marek Karpinski
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  3. Thomas Lickteig
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Bürgisser, P., Karpinski, M. & Lickteig, T. Some computational problems in linear algebra as hard as matrix multiplication. Comput Complexity 1, 131–155 (1991). https://doi.org/10.1007/BF01272518

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  • DOI: https://doi.org/10.1007/BF01272518

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