Gaussian elimination is not optimal

@article{Strassen1969GaussianEI,
  title={Gaussian elimination is not optimal},
  author={Volker Strassen},
  journal={Numerische Mathematik},
  year={1969},
  volume={13},
  pages={354-356}
}
  • V. Strassen
  • Published 1 August 1969
  • Mathematics
  • Numerische Mathematik
t. Below we will give an algorithm which computes the coefficients of the product of two square matrices A and B of order n from the coefficients of A and B with tess than 4 . 7 n l°g7 arithmetical operations (all logarithms in this paper are for base 2, thus tog 7 ~ 2.8; the usual method requires approximately 2n 3 arithmetical operations). The algorithm induces algorithms for invert ing a matr ix of order n, solving a system of n linear equations in n unknowns, comput ing a determinant of… 
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    IEEE Transactions on Computers
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TLDR
A new way of computing the inner product of two vectors is described that can be performed using roughly n3/2 multiplications instead of the n3multiplications which the regular method necessitates.
Seminar fiir angewandte Mathematik der Universit~tt 8032 Ziirich, Freie Str
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