Textbook: Mathematical Methods in the Physical Sciences by Mary L. Boas

3. a) Let U be a unitary matrix with eigenvectors [v) and eigenvalues A. Act Uf on the equation U|v) = Alv) to show that U has the same eigenvectors as U. What are the corresponding eigenvalues? b) Evaluate (Uvv) = (Uv)Tv in two different ways to find a condition on the values 1. c) What can you say about eigenvalues of orthogonal matrices