grandes-ecoles 2018 Q2

grandes-ecoles · France · centrale-maths1__psi Matrices Matrix Algebra and Product Properties

Show that if two matrices $A$ and $B$ commute $(AB = BA)$ and if $P$ and $Q$ are two polynomials of $\mathbb{C}[X]$, then $P(A)$ and $Q(B)$ commute.

Show that if two matrices $A$ and $B$ commute $(AB = BA)$ and if $P$ and $Q$ are two polynomials of $\mathbb{C}[X]$, then $P(A)$ and $Q(B)$ commute.