In the Google matrix where $$G=\alpha A+(1-\alpha)\frac{1}{n}ee^T$$
and $e$ is a vector of ones, how do I show that $e$ is the eigenvector of $G^T$ corresponding to the eigenvalue of 1
I need to show that $G^Te=e$ right?
I get $G^Te=(\alpha A^T+(1-\alpha)\frac{1}{n}e^Te)e$, not sure how to proceed from there.