grandes-ecoles 2019 Q12

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

Let $A$ denote a matrix in $\mathcal{M}_n(\mathbb{C})$.
Show that, if $A$ is nilpotent, then 0 is the unique eigenvalue of $A$.

Let $A$ denote a matrix in $\mathcal{M}_n(\mathbb{C})$.

Show that, if $A$ is nilpotent, then 0 is the unique eigenvalue of $A$.