Suppose I have a matrix $A$. We can assume, if it will be relevant, that it is stochastic with entries in $\{0,\frac{1}{2},\frac{3}{4},1\}$ and eigenvalues with magnitudes in $(0,1]$.
$A$ has a Jordan decomposition $A = VJV^{-1}$. I would like to find an upper bound $\|V\|_{2}$ and $\|V^{-1}\|_{2}$.
I know that I can take $V$ to be a generalized eigenvector basis, so a crude bound for $\|V\|_{F}$ can be $n^{2}$, implying $\|V\|_{2} \le n^{3}$. If so, what about $\| V^{-1} \|$? Any bound (w.r.t. $n$) will be useful.
Thank you very much.