Approximation of real matrices by integral matrices

  title={Approximation of real matrices by integral matrices},
  author={Glyn Harman},
  • Glyn Harman
  • Published 1990
  • Mathematics
  • It is shown that, given a k × k real matrix (αij) with determinant one, and a positive integer n, there exist integral matrices (Aij) with det Aij = n, such that |n1kαij − Aij| < Cn34k for all i and j. It is also demonstrated that the exponent 34k cannot be replaced by a number smaller than 12k. 

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