A classic symmetric eigenvalue test problem.

  This matrix was a challenge for many matrix eigenvalue algorithms.

  But the Francis QRM02QU2 algorithm, as perfected by Wilkinson and 

  implemented in EISPACK and MATLAB has no trouble with it.

  The matrix is 8-by-8 with integer elements.

  It has:

      * A double eigenvalue.

      * Three nearly equal eigenvalues.

      * Dominant eigenvalues of opposite sign.

      * A zero eigenvalue.

      * A small, nonzero eigenvalue.