In a proof I am trying to understand, the following is stated:
$ M$ is a non-random matrix with eigenvalues $\lambda_i$, $v$ is a random vector, $n$ is a scalar,
$\operatorname{Var}(M^n v) \ge \max(|\lambda_i|)^n $
As I copied this from the blackboard, I might have made a mistake. Our script says
$\ \lim_{n\to\infty}\operatorname{Var}(M^n v) = \infty \mbox{ if } \max(|\lambda_i|) > 1 $
(which would be implied by the first inequality).
If anyone could explain why this holds, or point me to a paper/book where this is explained I would very much appreciate it.