 In general, there are nine degrees of freedom in any unitary three by three matrix.However, in the case of the PMNS matrix five of those real parameters can be absorbed as phases of the lepton fields and thus the PMNS matrix can be fully described by four free parameters.The PMNS matrix is most commonly parameterized by three mixing angles (formula_14, formula_15, and formula_16) and a single phase angle called formula_17 related to charge-parity violations (i.e.