Eigenvalues/Endomorphism/Matrix/Fact/Proof

This follows directly from fact  (1), using the diagram

${\displaystyle {\begin{matrix}V&{\stackrel {\varphi }{\longrightarrow }}&V&\\\!\!\!\!\!\!\!\!\!\!\!\!\!\psi _{\mathfrak {u}}^{-1}\downarrow &&\downarrow \!\psi _{\mathfrak {u}}^{-1}\!\!\!\!\!&\\K^{n}&{\stackrel {M_{\mathfrak {u}}^{\mathfrak {u}}(\varphi )}{\longrightarrow }}&K^{n}\,.&\!\!\!\!\!\\\end{matrix}}}$