APPENDIX A

Changing Primaries

This appendix describes the operation of transforming one set of primaries into another. The mathematical name for this operation is a change of basis.

To convert a color from one set of primary lights to another, it is first necessary to define a conversion between the primaries themselves. We can think of this as matching each of the new primary lights using the old primary system. Suppose we designate our original set of primaries P₁, P₂, and P₃ and the new set of primaries Q₁, Q₂, and Q₃. We now use our original primaries to create matches with each of the new primaries in turn. Let us call the amount of each of the P primaries c_ij .

Thus,

(A.1)

If we denote the matrix of c_ij values C, then

(A.2)

To reverse the transformation, invert the matrix:

(A.3)

This same matrix can now be used to convert any set of values expressed in one set of primaries to the other set of primaries. Thus, the values p₁ , p₂, and p₃ represent the amounts of the lights in primary system P needed to make a match.

(A.4)

Then we can calculate the values q in primary system Q simply by solving

(A.5)