Let $M$ be a cyclic matrix and $x_0$ be a cyclic vector of $f_M$. The set $\mathcal{C}(f_M) = \{g \in \mathcal{L}(\mathbb{C}^n) \mid f_M \circ g = g \circ f_M\}$ is sought to be shown to be the set of polynomials in $f_M$. Conclude.
Let $M$ be a cyclic matrix and $x_0$ be a cyclic vector of $f_M$. The set $\mathcal{C}(f_M) = \{g \in \mathcal{L}(\mathbb{C}^n) \mid f_M \circ g = g \circ f_M\}$ is sought to be shown to be the set of polynomials in $f_M$. Conclude.