2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217919We 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 show that by using these invariants the ansatz such as $μ-τ$ exchange and reflection symmetries, various texture zeros and flavor symmetries can be expressed in a general basis.19 pages, Version appeared in Nuclear Physics BHigh Energy Physics - Phenomenologytext