grandes-ecoles 2017 QI.C.1

grandes-ecoles · France · centrale-maths1__mp Invariant lines and eigenvalues and vectors Eigenvalue and Characteristic Polynomial Analysis
Let $A \in \mathrm{O}_{n}(\mathbb{R})$. Show that the eigenvalues of $A_{s}$ are in $[-1,1]$. 
Let $A \in \mathrm{O}_{n}(\mathbb{R})$. Show that the eigenvalues of $A_{s}$ are in $[-1,1]$.
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