HW9

1)  Use your QR Factorization code to implement the 
QR scheme without shift to compute the eigenvalueis
of a matrix.  It should be implemented as a function or
procedure taking the matrix and return the eigenvalues.

Test your code on a small symmetric floating point
matrix of your choice.


2) Modify the above procedure to incorporate a shift to improve the
convergence by incorporating a shift. Test your code on a small 
symmetric floating point matrix of your choice.

3) Test both the procedures on small non-symettric matrices.

4) Try to develop a scheme to approximate an eigenvalue near a specific 
location using the "shift" idea.