Form invariance of the neutrino mass matrix

Consider the most general 3 x 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 not equal 1 is a specific unitary matrix such that U(N) represents a well-defined discrete symmetry in the nu(e,micro,tau) 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.