  The evidence for neutrino oscillations implies that three neutrino flavors
(\nu_e, \nu_\mu, \nu_\tau) must have different mass states (\nu_1, \nu_2,
\nu_3). The most popular idea of generating tiny masses of \nu_i is to
introduce three heavy Majorana neutrinos N_i (for i = 1, 2, 3) into the
standard model and implement the seesaw mechanism. In this approach the
neutrino mixing matrix V appearing in the charged current interactions of \nu_i
is not unitary, and the strength of unitarity violation of V is associated with
the matrix R which describes the strength of charged current interactions of
N_i. We present an explicit parametrization of the correlation between V and R
in terms of nine rotation angles and nine phase angles, which can be measured
or constrained in the precision neutrino oscillation experiments and by
exploring possible signatures of N_i at the LHC and ILC. Two special but viable
scenarios, the Type-I seesaw model with two heavy Majorana neutrinos and the
Type-II seesaw model with one heavy Majorana neutrino and one Higgs triplet,
are taken into account to illustrate the simplified V-R correlation. The
implications of R \neq 0 on the low-energy neutrino phenomenology are also
discussed. In particular, we demonstrate that the non-unitarity of V is
possible to give rise to an appreciable CP-violating asymmetry between \nu_\mu
-> \nu_\tau and \bar{\nu}_\mu -> \bar{\nu}_\tau oscillations with short or
medium baselines.
