  Assuming the existence of one light sterile neutrino, we investigate the
neutrino flavor mixing matrix in matter. Sum rules between the mixing
parameters in vacuum and their counterparts in matter are derived. By using
these new sum rules, we obtain the simple but exact expressions of the
effective flavor mixing matrix in matter in terms of neutrino masses and the
mixing parameters in vacuum. The rephasing invariants, sides of unitarity
quadrangles and oscillation probabilities in matter are also achieved. Our
model-independent results will be very helpful for analyzing flavor mixing and
CP violation in the future long-baseline neutrino oscillation experiments.
