Why does $v_1^T \lambda_1 v_1 = \lambda_1$

Question

Let $v_1$ an eigenvector and let $\lambda_1$ it's eigenvalue. Why is it true that:$v_1^T \lambda_1 v_1 = \lambda_1$?

I'm asking it to udnerstand the Power Method algorithm.
In this method, $q^{(k)}$ converges to $v_1$.

Answer 1

This is obviously only true for a unit vector $v_1$ as then $v_1^Tv_1=1$. This normalization you should find as part of the algorithm.