For every $x \in E$, we denote by $\omega ( x , \cdot )$ the linear map from $E$ to $\mathbb { R }$, $y \mapsto \omega ( x , y )$ and we consider
$$d _ { \omega } : \left\lvert \, \begin{array} { c c c }
E & \rightarrow & \mathcal { L } ( E , \mathbb { R } ) \\
x & \mapsto & \omega ( x , \cdot )
\end{array} \right.$$
Show that $d _ { \omega }$ is an isomorphism.