A classic symmetric eigenvalue test problem.
This matrix was a challenge for many matrix eigenvalue algorithms.
But the Francis QR 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.
* A double eigenvalue.
* Three nearly equal eigenvalues.
* Dominant eigenvalues of opposite sign.
* A zero eigenvalue.
* A small, nonzero eigenvalue.