grandes-ecoles 2010 QI.C.2

grandes-ecoles · France · centrale-maths2__psi Groups Decomposition and Basis Construction

Let $V$ be a vector subspace of $\mathscr{L}(E)$ included in $\operatorname{Sim}(E)$. We fix $x \in E \backslash \{0\}$. By considering $\Phi : f \mapsto f(x)$, linear application from $V$ to $E$, show that $\operatorname{dim}(V) \leqslant n$. Thus $1 \leqslant d_{n} \leqslant n$.

Let $V$ be a vector subspace of $\mathscr{L}(E)$ included in $\operatorname{Sim}(E)$. We fix $x \in E \backslash \{0\}$. By considering $\Phi : f \mapsto f(x)$, linear application from $V$ to $E$, show that $\operatorname{dim}(V) \leqslant n$. Thus $1 \leqslant d_{n} \leqslant n$.

Paper Questions

QI.A.1 QI.A.2 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.C.1 QI.C.2 QI.C.3 QI.C.4 QI.C.5 QI.D.1 QI.D.2 QI.D.3 QI.D.4 QII.A.1 QII.A.2 QII.B.1 QII.B.2 QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.C.5 QII.C.6 QII.D QII.E