1. The problem statement, all variables and given/known data U is a unitary matrix. Show that ||UX|| = ||X|| for all X in the complex set. Also show that |λ| = 1 for every eigenvalue λ of U. 2. Relevant equations 3. The attempt at a solution I'm not sure where to start. So I looked up the definition of a unitary matrix. It satisfies one of these conditions: U-1 = UH The rows of U are an orthonormal set in the complex set The columns of U are an orthonormal set in the complex set Say X = [x1 x2 ... xn] Now I know that ||X||2 = <X, X> = |x1|2 ... |xn|2 I'm not sure where to go from here. Can anyone help?