grandes-ecoles 2013 QIII.C.1

grandes-ecoles · France · centrale-maths2__psi Matrices Diagonalizability and Similarity

Let $A, B \in M_p(\mathbb{K})$ be two diagonalizable matrices. We assume that $A$ and $B$ commute.
Show that there exists $P \in GL_p(\mathbb{C})$ such that $P^{-1}AP$ and $P^{-1}BP$ are diagonal.
(We shall study the restrictions of $u_B$ to the eigenspaces of $u_A$.)

Let $A, B \in M_p(\mathbb{K})$ be two diagonalizable matrices. We assume that $A$ and $B$ commute.

Show that there exists $P \in GL_p(\mathbb{C})$ such that $P^{-1}AP$ and $P^{-1}BP$ are diagonal.

(We shall study the restrictions of $u_B$ to the eigenspaces of $u_A$.)

Paper Questions

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