I have a (non-sparse) $9 \times 9$ matrix and I wish to obtain its eigenvalues and eigenvectors. Of course, the eigenvalues can be quite a pain as we will probably not be able to find the zeros of its characteristic polynomial.
Actually, what I really want is find the eigenvector belonging to the largest eigenvalue. Would the following code give me this:
How does Mathematica do this? Is there some kind of algorithm of which's existence I am unaware that computes the eigenvector belonging to the largest eigenvalue?
Can the largest eigenvalue be computed numerically (in modulus or even throw away all the complex ones), and then the eigenvectors pseudo-analytically using
Added: The matrix is symbolical.