Power vectors versus power matrices, and the mathematical nature of dioptric power.

Representation of astigmatic dioptric power as a power vector is satisfactory for basic operations such as summing and averaging powers. However, power vectors do not fully characterize the nature of dioptric power and are, therefore, unsatisfactory for representing power in general. The purpose of this note is to make the case that it is the power matrix instead that is proper for the representation of power in general. The mathematical nature of dioptric power is examined.