Eigenvalue/Dual mapping/Exercise

Let

$\varphi \colon V\longrightarrow V$

be an endomorphism on a finite-dimensional ${}K$-vector space ${}V$, and let ${}a\in K$ an eigenvalue of ${}\varphi$. Show that ${}a$ is also an eigenvalue of the dual mapping

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

Create a solution