grandes-ecoles 2017 QII.E.1

grandes-ecoles · France · centrale-maths1__official Matrices Linear Transformation and Endomorphism Properties

Let $F$ be a vector subspace of $E_{n}$ of dimension $n-p$, where $1 \leqslant p \leqslant n-1$. Show that $A$ is $F$-singular if $\operatorname{det}\left(N^{\prime\top} A N^{\prime}\right) = 0$ for a matrix $N^{\prime} \in \mathcal{G}_{n,p}(\mathbb{R})$ that one will define.

Let $F$ be a vector subspace of $E_{n}$ of dimension $n-p$, where $1 \leqslant p \leqslant n-1$. Show that $A$ is $F$-singular if $\operatorname{det}\left(N^{\prime\top} A N^{\prime}\right) = 0$ for a matrix $N^{\prime} \in \mathcal{G}_{n,p}(\mathbb{R})$ that one will define.

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 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.A.5 QII.A.6 QII.A.7 QII.A.8 QII.B.1 QII.B.2 QII.B.3 QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.C.5 QII.C.6 QII.C.7 QII.C.8 QII.D.1 QII.D.2 QII.E.1 QII.E.2 QII.E.3 QII.E.4 QII.E.5 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C.1 QIII.C.2 QIII.C.3