Endomorphism/Dual mapping/Trigonalizable/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, and let

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

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

Create a solution