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Some computational problems in linear algebra as hard as matrix multiplication


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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Bürgisser, P., Karpinski, M. & Lickteig, T. Some computational problems in linear algebra as hard as matrix multiplication. Comput Complexity 1, 131–155 (1991).

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Key words

  • Problems
  • computation trees
  • straight line programs
  • Ostrowski complexity
  • derivations
  • matrix multiplication

Subject classifications

  • 68C20
  • 68C25