There is a matrix as following,

A=[0 0 0 1;b 0 0 a;ab b 0 $a^2$; $a^2b$ ab b $a^{N-1}$],

where $A \in \mathbf{R^4}$, $a,b \in \mathbf{R}$, and $|a|,|b|<1$ Then how to estimate the norm or the eigenvalue of $A$ and $A^k$, where $k \in \mathbf{N^{+}}$.Furthermore, when $A \in \mathbf{R^n}$, then how to estimate.

Great thanks!