We denote $C = \left\{ U \in \mathcal{M}_{n,1}(\mathbb{R}) \mid U^\top U = 1 \right\}$. Deduce that the application $U \mapsto \left| U^\top A U \right|$ admits a maximum on $C$.
We denote $C = \left\{ U \in \mathcal{M}_{n,1}(\mathbb{R}) \mid U^\top U = 1 \right\}$. Deduce that the application $U \mapsto \left| U^\top A U \right|$ admits a maximum on $C$.