I am currently stuck on the following proof.
Suppose that a (n by n) unitary matrix U can be written as U=M+iN where M and N are Hermitian matrices.
Now assuming that M and N have n distinct eigenvalues it can be shown that they have the same eigenvectors.
My attempts to show it have been unsuccessful. I was wondering whether any one could give me advice on how to do this because I am getting nowhere at the moment.