  A generalized connection between the quantum mechanical Bargmann invariants
and the geometric phases was established for the Dirac fermions. We extend that
formalism for the Majorana fermions by defining proper quantum mechanical ray
and Hilbert spaces. We then relate both the Dirac and Majorana type Bargmann
invariants to the rephasing invariant measures of CP violation with the
Majorana neutrinos, assuming that the neutrinos have lepton number violating
Majorana masses. We then generalize the recursive parametrization for studying
any unitary matrices to include the Majorana fermions, which could be useful
for studying the neutrino mixing matrix.
