We denote $C = \left\{ U \in \mathcal{M}_{n,1}(\mathbb{R}) \mid U^\top U = 1 \right\}$. Show that $\rho(A) \leqslant \max_{U \in C} \left| U^\top A U \right|$.
We denote $C = \left\{ U \in \mathcal{M}_{n,1}(\mathbb{R}) \mid U^\top U = 1 \right\}$. Show that $\rho(A) \leqslant \max_{U \in C} \left| U^\top A U \right|$.