grandes-ecoles 2023 Q23

grandes-ecoles · France · centrale-maths1__official Invariant lines and eigenvalues and vectors Diagonalizability determination or proof
Let $T$ be a delta endomorphism of $\mathbb{K}[X]$. For $n \in \mathbb{N}$, we denote by $T_n$ the restriction of $T$ to $\mathbb{K}_n[X]$.
Show that $T_n$ is an endomorphism of $\mathbb{K}_n[X]$. Is it diagonalizable?
Let $T$ be a delta endomorphism of $\mathbb{K}[X]$. For $n \in \mathbb{N}$, we denote by $T_n$ the restriction of $T$ to $\mathbb{K}_n[X]$.

Show that $T_n$ is an endomorphism of $\mathbb{K}_n[X]$. Is it diagonalizable?