  In the flavor basis where the mass eigenstates of three charged leptons are
identified with their flavor eigenstates, one may diagonalize a 3 X 3 Majorana
neutrino mass matrix M_nu by means of the standard parametrization of the 3 X 3
neutrino mixing matrix V. In this treatment the unphysical phases of M_nu have
to be carefully factored out, unless a special phase convention for neutrino
fields is chosen so as to simplify M_nu to M'_nu without any unphysical phases.
We choose this special flavor basis and establish some exact analytical
relations between the matrix elements of M'_nu M'_nu^dag and seven physical
parameters --- three neutrino masses (m_1, m_2, m_3), three flavor mixing
angles (theta_12, theta_13, theta_23) and the Dirac CP-violating phase (delta).
Such results allow us to derive the conditions for the mu-tau flavor symmetry
with theta_23 = pi/4 and maximal CP violation with delta = +/- pi/2, which
should be useful for discussing specific neutrino mass models. In particular,
we show that theta_23 = pi/4 and delta = +/- pi/2 keep unchanged when constant
matter effects are taken into account for a long-baseline neutrino oscillation
experiment.
