A Hilbert matrix with the first row replaced by ones. It is unsymmetric, ill conditioned, totally positive, and has many small, negative eigenvalues. The inverse has integer entries and is known explicitly.


  1. This generator is adapted from Nicholas J. Higham's Test Matrix Toolbox.
  2. M. Lotkin, A set of test matrices, MTAC, 9 (1955), pp. 153-161.

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