grandes-ecoles 2013 QIV.B.2

grandes-ecoles · France · centrale-maths2__pc Invariant lines and eigenvalues and vectors Compute eigenvectors or eigenspaces

In this section we consider a circle $\mathcal{C}(\Omega, r)$ with center $\Omega$ and non-zero radius $r$, tangent to the $x$-axis. We call $L$, with coordinates $(\lambda, 0)$, the point of tangency of $\mathcal{C}(\Omega, r)$ with the $x$-axis. Let $A$ be a matrix whose eigenvalue circle equals $\mathcal{C}(\Omega, r)$. We keep the notations $E, F, G, H$ from III.D.
Can we give an eigenvector using the points $L, E, F, G$ and $H$?

In this section we consider a circle $\mathcal{C}(\Omega, r)$ with center $\Omega$ and non-zero radius $r$, tangent to the $x$-axis. We call $L$, with coordinates $(\lambda, 0)$, the point of tangency of $\mathcal{C}(\Omega, r)$ with the $x$-axis. Let $A$ be a matrix whose eigenvalue circle equals $\mathcal{C}(\Omega, r)$. We keep the notations $E, F, G, H$ from III.D.

Can we give an eigenvector using the points $L, E, F, G$ and $H$?

Paper Questions

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