Form Invariance of the Neutrino Mass Matrix

Consider the most general 3×3 Majorana neutrino mass matrix M. Motivated by present neutrino-oscillation data, much theoretical effort is directed at reducing it to a specific texture in terms of a small number of parameters. This procedure is often ad hoc. I propose instead that for any M one may choose, it should satisfy the condition UMU^T=M, where U≠1 is a specific unitary matrix such that U^N represents a well-defined discrete symmetry in the ν_e,μ,τ basis, N being a particular integer not necessarily equal to 1. I illustrate this idea with a number of examples, including the realistic case of an inverted hierarchy of neutrino masses.