The asymptotic spectrum of tensors and the exponent of matrix multiplication

  • Authors:

  • V. Strassen

  • Affiliations:

  • -

  • Venue:
  • SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1986

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Abstract

We introduce an asymptotic data structure for the relative bilinear complexity of bilinear maps (tensors). It consists of a compact Hausdorff space Δ together with an interpretation of the tensors under consideration as continuous functions on Δ. The asymptotic rank of a tensor is simply the maximum of the associated function. On the way we present a new method for estimating the exponent ω of matrix multiplication, leading at present to the bound ω