Diagonalizable/Dual mapping/Exercise

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

$\varphi \colon V\longrightarrow V$

be a linear mapping. Let

${\varphi }^{*}\colon {V}^{*}\longrightarrow {V}^{*}$

denote the dual mapping. Show that ${}\varphi$ is diagonalizable if and only if ${}{\varphi }^{*}$ is diagonalizable.

Create a solution