Let $A, B \in \mathcal{M}_n(\mathbb{C})$. Suppose that there exists a unitary matrix $U \in \mathcal{M}_n(\mathbb{C})$ such that $B = UAU^{-1}$. Show that $\|A\| = \|B\|$.
Let $A, B \in \mathcal{M}_n(\mathbb{C})$. Suppose that there exists a unitary matrix $U \in \mathcal{M}_n(\mathbb{C})$ such that $B = UAU^{-1}$. Show that $\|A\| = \|B\|$.