grandes-ecoles 2010 QI.C.5

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

Let $V$ be a vector subspace of $\mathscr{L}(E)$ included in $\operatorname{Sim}(E)$, of dimension $d \geqslant 1$. Show that there exists a vector subspace $W$ of $\mathscr{L}(E)$ included in $\operatorname{Sim}(E)$, of the same dimension $d$, and containing $\operatorname{Id}_{E}$.

Let $V$ be a vector subspace of $\mathscr{L}(E)$ included in $\operatorname{Sim}(E)$, of dimension $d \geqslant 1$. Show that there exists a vector subspace $W$ of $\mathscr{L}(E)$ included in $\operatorname{Sim}(E)$, of the same dimension $d$, and containing $\operatorname{Id}_{E}$.

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