Matrix/Nilpotent/Definition

Nilpotent matrix

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

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