grandes-ecoles 2013 QI.B.1

grandes-ecoles · France · centrale-maths2__pc Invariant lines and eigenvalues and vectors Properties of eigenvalues under matrix operations

Let $A, B \in \mathcal{M}_n(\mathbb{R})$ and $P \in \mathrm{GL}_n(\mathbb{R})$ such that $B = P^{-1}AP$. Show that $f_A$ and $f_B$ have the same eigenvalues.

Let $A, B \in \mathcal{M}_n(\mathbb{R})$ and $P \in \mathrm{GL}_n(\mathbb{R})$ such that $B = P^{-1}AP$. Show that $f_A$ and $f_B$ have the same eigenvalues.

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