Is there any ways to compute the eigen vector without computing explicitly the associated eigenvalue?


Actually, I'd like to compute the largest eigenvalue of a positive matrix from its eigen vector, so I have to know its eigenvector first.



can eigenvector be found without computing the eigenvalue
If you pick a random vector $v$ and look at $v\_n=A^n v/\| A^n v\|,$ that will converge to the dominant eigenvector.


