All-purpose neutrino mass matrix

A four-parameter Majorana neutrino mass matrix is proposed, which is exactly diagonalizable with two mixing angles, one of which is $\pi /4\mathrm{}$ and the other large but less than $\pi /4.\mathrm{}$ The form of this mass matrix allows seven realizations of the present data on atmospheric and solar neutrino oscillations: three have the normal hierarchy, two have the inverse hierarchy, and two have three nearly degenerate masses. The possible inclusion of $\mathrm{CP}$ violation is also discussed.