Dimostrazione.
Sia $\lambda \in \mathbf{R}$ tale che $\forall \mathbf{v} \in \mathbf{E}, \quad f(\mathbf{v})= \lambda \mathbf{v}$. Allora
$\vert\vert\mathbf{v}\vert\vert=\vert\vert f(\mathbf{v})\vert\vert=\vert\vert \l...
...vert \, \vert\lambda\vert \quad \Rightarrow \quad \vert \lambda \vert=1, \quad $ cioè $ \,\, \lambda = \pm 1$.
c.v.d.