Neutrino Mass Hierarchies in a Mass Matrix Form Versus its Inverse Form

A neutrino mass matrix model M_\nu with M_\nu^T =M_\nu and a model with its inverse matrix form \widetilde{M}_\nu = m_0^2 (M_\nu^*)^{-1} can be diagonalized by the same mixing matrix U_\nu. It is investigated whether a scenario which provides a matrix model M_\nu with normal mass hierarchy can also give a model with an inverted mass hierarchy by considering a model with an inverse form of M_\nu.