** 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. **

** It has: **

** * A double eigenvalue. **

** * Three nearly equal eigenvalues. **

** * Dominant eigenvalues of opposite sign. **

** * A zero eigenvalue. **

** * A small, nonzero eigenvalue. **

** **