grandes-ecoles 2017 QII.E.1

grandes-ecoles · France · centrale-maths2__psi Invariant lines and eigenvalues and vectors Compute eigenvalues of a given matrix
We denote $Q = A _ { p - 1 } A _ { p - 2 } \cdots A _ { 0 }$. Prove that (II.2) admits a nonzero periodic solution of period $p$ if and only if 1 is an eigenvalue of $Q$. 
We denote $Q = A _ { p - 1 } A _ { p - 2 } \cdots A _ { 0 }$. Prove that (II.2) admits a nonzero periodic solution of period $p$ if and only if 1 is an eigenvalue of $Q$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.A.5 QII.B.1 QII.B.2 QII.B.3 QII.C QII.D.1 QII.D.2 QII.E.1 QII.E.2 QII.E.3 QIII.A QIII.B.1 QIII.B.2 QIII.C QIII.D.1 QIII.D.2 QIII.E.1 QIII.E.2 QIII.E.3 QIV.A.1 QIV.A.2 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QV.A QV.B.1 QV.B.2 QV.B.3 QV.B.4