  We propose a model-independent analysis of the neutrino mass matrix through
an expansion in terms of the eigenvectors defining the lepton mixing matrix,
which we show can be parametrized as small perturbations of the tribimaximal
mixing eigenvectors. This approach proves to be powerful and convenient for
some aspects of lepton mixing, in particular when studying the sensitivity of
the mass matrix elements to departures from their tribimaximal form. In terms
of the eigenvector decomposition, the neutrino mass matrix can be understood as
originating from a tribimaximal dominant structure with small departures
determined by data. By implementing this approach to cases when the neutrino
masses originate from different mechanisms, we show that the experimentally
observed structure arises very naturally. We thus claim that the observed
deviations from the tribimaximal mixing pattern might be interpreted as a
possible hint of a ``hybrid'' nature of the neutrino mass matrix.
