A selection of ill conditioned matrices. Examples B and C are nearly diagonal (they must be at least order 4 and 3, respectively). The parameter Theta is a linear contribution to elements in Example B, and appears as 1/Theta and 1/Theta^2 in Example C. Example D is a lower triangular matrix with 1's on the diagonal and -1's on the off-diagonals; it depends only on the Order.


These matrices provide `counter-examples' to the LINPACK condition number estimator.


  1. This generator is adapted from Nicholas J. Higham's Test Matrix Toolbox.
  2. A.K. Cline and R.K. Rew, A set of counter-examples to three condition number estimators, SIAM J. Sci. Stat. Comput., 4 (1983), pp. 602-611.

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