Matrix/Nilpotent/Definition

A square matrix ${\displaystyle {}M}$ is called nilpotent, if there exists a natural number ${\displaystyle {}n\in \mathbb {N} }$ such that the ${\displaystyle {}n}$-th matrix product fulfills

${\displaystyle {}M^{n}=\underbrace {M\circ \cdots \circ M} _{n{\text{-mal}}}=0\,}$