With the same setup as Q27 (matrices $A$, $B$, $I_q$, $r$, $F_n$), show that the sequence $\left(F_{n}\right)_{n \in \mathbb{N}}$ is bounded regardless of the choice of $F_{0}$ if and only if the eigenvalues of $A$ belong to $[-1, 1]$.
With the same setup as Q27 (matrices $A$, $B$, $I_q$, $r$, $F_n$), show that the sequence $\left(F_{n}\right)_{n \in \mathbb{N}}$ is bounded regardless of the choice of $F_{0}$ if and only if the eigenvalues of $A$ belong to $[-1, 1]$.