grandes-ecoles 2022 Q7

grandes-ecoles · France · centrale-maths1__mp Proof Proof That a Map Has a Specific Property

For $\ell \in \mathcal { L } ( E , \mathbb { R } )$, we denote by $\left. \ell \right| _ { F }$ the restriction of $\ell$ to $F$. Show that the restriction map $r _ { F } : \begin{array} { c c c } \mathcal { L } ( E , \mathbb { R } ) & \rightarrow & \mathcal { L } ( F , \mathbb { R } ) \\ \ell & \mapsto & \left. \ell \right| _ { F } \end{array}$ is surjective.

For $\ell \in \mathcal { L } ( E , \mathbb { R } )$, we denote by $\left. \ell \right| _ { F }$ the restriction of $\ell$ to $F$. Show that the restriction map $r _ { F } : \begin{array} { c c c } \mathcal { L } ( E , \mathbb { R } ) & \rightarrow & \mathcal { L } ( F , \mathbb { R } ) \\ \ell & \mapsto & \left. \ell \right| _ { F } \end{array}$ is surjective.

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