The asymptotic spectrum of tensors and the exponent of matrix multiplication

@article{Strassen1986TheAS,
  title={The asymptotic spectrum of tensors and the exponent of matrix multiplication},
  author={Volker Strassen},
  journal={27th Annual Symposium on Foundations of Computer Science (sfcs 1986)},
  year={1986},
  pages={49-54}
}
  • V. Strassen
  • Published 27 October 1986
  • Computer Science, Mathematics
  • 27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
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 ≪ 2.48. The paper gives only brief… 
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Tensor rank is not multiplicative under the tensor product
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