grandes-ecoles 2019 Q6

grandes-ecoles · France · centrale-maths1__official Invariant lines and eigenvalues and vectors Diagonalizability determination or proof

Let $f$ be a cyclic endomorphism. Show that $f$ is diagonalisable if and only if $\chi_f$ is split over $\mathbb{K}$ and has all its roots simple.

Let $f$ be a cyclic endomorphism. Show that $f$ is diagonalisable if and only if $\chi_f$ is split over $\mathbb{K}$ and has all its roots simple.