I'm trying to properly get to know the Jordan normal form Theorem, and am confused as to why this proposition holds. I have read that if A is a matrix in Jordan normal form and $T:V\rightarrow V$ then $$\dim\ker(T-\lambda I)^r-\dim\ker(T-\lambda I)^{r-1}$$ is the number of Jordan blocks $J_m(\lambda)$ of A with $m\geq r$.
I am not sure why this holds, can anyone explain this for me?