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At the zeroth order, degenerate neutrino mass matrices can be considered
as a sum of hierarchial and inverse hierarchial sub matrices.
This holds true irrespective of the kind of mixing present in each sub
matrix. Such decomposition is natural in Type I and Type III seesaw
mechanisms. We show that in two generations, the degeneracy requirement
can ensure maximal mixing even if the individual sub matrices
contain only small mixing. In three generations, a straight forward
extension of this `degeneracy induced large mixing' can lead to
maximally symmetric mixing matrix with three large mixing angles. A more
suitable decomposition with two sub matrices is
presented where this mechanism can be used to generate one large mixing
while keeping another small. On the other hand, the proposed mechanism can
have realizations in terms of hybrid seesaws i.e., where there is more
than one seesaw mechanism at work. The left right symmetric model where
both Type I and Type II are simultaneously present provides a natural
setting for realization of the above mechanism.