Diagonalizable/Generalized eigenspace/Exercise

Show that for a diagonalizable mapping

${\displaystyle \varphi \colon V\longrightarrow V}$

and every ${\displaystyle {}\lambda \in K}$, the equality

${\displaystyle {}\operatorname {Eig} _{\lambda }{\left(\varphi \right)}=\operatorname {GeEig} _{\lambda }(\varphi )\,}$

holds.