Nilpotent

Definition

A linear transform $T:V\to V$ is nilpotent $⟺$ $\exists n>1$ s.t $\forall v\in V,T^n(v)=0$

Example

With matrix

$$A=\left[\begin{array}{cc}2& 1\\ 0& 2\end{array}\right]$$

The nilpotent

$$N=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]$$