Endomorphism/Nilpotent/Definition

Nilpotent endomorphism

Let ${}K$ be a field, and let ${}V$ be a ${}K$-vector space. A linear mapping

$\varphi \colon V\longrightarrow V$

is called nilpotent, if there exists a natural number ${}n$ such that the ${}n$-th composition fulfills

${}\varphi ^{n}=0\,.$