Example 3.  Find the dominant eigenvalue and eigenvector for the matrix  .  
Use the shift   in the shifted inverse power method.

Solution 3.

That is close to the dominant eigenvalue    and corresponding eigenvector  .  

Now check our work.

Compare with Mathematica's Eigensystem procedure.  Observe that Mathematica returns unit length eigenvectors.

Notice.  The numerical eigenvector found by Mathematica is which is a multiple of the the eigenvector   found by the power method, i.e.

        

(c) John H. Mathews 2004