Chapter 3.11, Problem 61P

At the end of Section 9 we proved that if H is a Hermitian matrix, then the matrix $e^{iH}$ is unitary. Give another proof by writing $\text{H}={\text{CDC}}^{-1},$ remembering that now C is unitary and the eigenvalues in D are real. Show that $e^{iD}$ is unitary and that $e^{iH}$ is a product of three unitary matrices. See Problem 9.17d.