Generalizing Long's inversion of the matrix form of Prentice's equation and the concept of generalized inverse dioptric power.

The concept of generalized inverse dioptric power is introduced. Its use is illustrated in solving Long's matrix generalization of Prentice's equation for the decentration required to produce a specified prismatic effect. The solution holds in all cases for which a solution exists, including for the pure cylinder, and the result gives all solutions when more than one exists.