Endomorphism/Nilpotent/Diagonalizable/0/Exercise

Let ${}K$ be a field, and let ${}V$ denote a finite-dimensional ${}K$-vector space. Let

$\varphi \colon V\longrightarrow V$

be a nilpotent linear mapping. Suppose that ${}\varphi$ is diagonalizable. Show

${}\varphi =0\,.$

Create a solution