Diagonalization of a Hermitian matrix and its application to neutrino mass matrix

We carry out diagonalization of a $3times3$ Hermitian matrix of which Real component and Imaginary part are commutative and apply it to Majorana neutrino mass matrix $M=M_ u M_ u^dagger$ which satisfies the same condition. It is shown in a model-independent way for the kind of matrix M of which Real component and Imaginary part are commutative that $delta = pmpi/2$ which implies the maximal strength of CP violation in neutrino oscillations. And we obtain the prediction $cos (2theta_{23})=0$ for this kind of M. It is shown that the kind of Hermitian Majorana neutrino mass matrix M has only five real parameters and furthermore, only one free real parameter (D or A) if using the measured values of three mixing angles and mass differences as input.