grandes-ecoles 2013 QIV.C

grandes-ecoles · France · centrale-maths2__psi Matrices Eigenvalue and Characteristic Polynomial Analysis

Let $A \in M_p(\mathbb{C})$ be nilpotent of order $k$.
Show that there exists a polynomial $Q \in \mathbb{C}[X]$ such that $Q(A) = E(A)$.

Let $A \in M_p(\mathbb{C})$ be nilpotent of order $k$.

Show that there exists a polynomial $Q \in \mathbb{C}[X]$ such that $Q(A) = E(A)$.