I have a n x n matrix. I would like to
(a) take successively higher powers of the matrix and then multiply by projection vectors until the resulting vectors differ by only a scalar factor.
(b) calculate the dominant eigenvalue of the matrix to compare to (a)
and (c) calculate, using the same tactic as in (a), the dominant right and left eigenvectors.
This is too much work to do by hand, so my question is: can anyone recommend a program/language or package that would be ideal for the above calculations?