Endomorphism/Conjugation/Polynomial substitution/Exercise

Let

$f\colon V\longrightarrow V$

be an endomorphism on a ${}K$-vector space ${}V$, and let

$g\colon V\longrightarrow V$

denote an isomorphism. Show that, for every polynomial ${}P\in K[X]$, the equality

${}gP(f)g^{-1}=P(gfg^{-1})\,$

holds.

Create a solution