grandes-ecoles 2019 Q2

grandes-ecoles · France · x-ens-maths__pc Matrices Matrix Norm, Convergence, and Inequality

Let $U \in \mathcal{M}_n(\mathbb{C})$ be a unitary matrix. Show that $\|Ux\|_2 = \|x\|_2$ for all $x \in \mathbb{C}^n$.

Let $U \in \mathcal{M}_n(\mathbb{C})$ be a unitary matrix. Show that $\|Ux\|_2 = \|x\|_2$ for all $x \in \mathbb{C}^n$.