# Math Help - endomorphism

1. ## endomorphism

Hello unfortunately I can not show that the application "u" below is an endomorphism of E, if you can help me you are welcome, thank you.

These data :
$u:f\in E \longrightarrow u(f)$ where $\forall x \in \mathbb{R}, u(f)(x)=xf^{'}(x)$

2. It would help if you told us what 'E' was! Since you have u(f)= xf'(x), it must be at least 'differentiable functions' but are there any other conditions? And what operations are you allowing? That is, are you thinking of E as a group, vector space or algebra?

3. Yes of course, excuse me E is a $\mathbb{R}$vector space