grandes-ecoles 2022 Q9

grandes-ecoles · France · centrale-maths1__pc Matrices Eigenvalue and Characteristic Polynomial Analysis

Show that, if $A$ is nilpotent, that is, if there exists $p \in \mathbb{N}^\star$ such that $A^p = 0_n$, then the spectral radius of $A$ is zero.

Show that, if $A$ is nilpotent, that is, if there exists $p \in \mathbb{N}^\star$ such that $A^p = 0_n$, then the spectral radius of $A$ is zero.