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We construct a new set of combinations from the mass matrices of
the charged leptons and neutrinos that are invariant under basis
transformation, hereafter {\it the} invariants. We use these
invariants to study various symmetries and neutrino mass textures
in a basis independent way. In particular, we express the criteria
for the CP-invariance of the lepton sector in terms of these
invariants. We show that by using these invariants the ansatz such
as various texture zeros or $\mu-\tau$ exchange and reflection
symmetries can be expressed in a general basis. In the end, we
extend our analysis to include seesaw mechanism and express the
combinations of the Yukawa couplings that give leptogenesis in
terms of a certain set of invariants.
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