Let $A_1, A_2 \in \mathcal M_n(\mathbb C)$ be two fixed matrices with characteristic polynomials \begin{align*} &p_{A_1}(t) = t^n + \alpha_{n-1} t^{n-1} + \dots + \alpha_0, \\ &p_{A_2}(t) = t^{n} + \beta_{n-1}t^{n-1} + \dots + \beta_0. \end{align*} There is a bijection $\pi$ between $\mathbb C^n$...