1. The problem statement, all variables and given/known data Show that the eigenvectors of a unitary transformation belonging to distinct eigenvalues are orthogonal. 2. Relevant equations I know that U+=U^-1 (U dagger = U inverse) 3. The attempt at a solution I tried using a similar method to the proof which shows that the eigenvectors of hermitian transformations belonging to distinct eigenvalues are orthogonal. So assume our eigenvectors are a and b. I assumed U(a)=xa and U(b)=yb x<a|b>=<Ua|b>=<a|U^-1b>= ??? Help anyone. I know this probably isn't too rough.