Color science applications of the Binet–Cauchy theorem

The Binet–Cauchy theorem, an expansion of the determinant of the product of two nonsquare matrices, is quite useful in deriving theorems about ordering relations in color science. The theorem is first described in a special case that proved suitable to color. Then an application of the theorem is described that finds the conditions among reflectance factors in a color atlas such that their chromaticity ordering is illuminant invariant. Finally, an application is described that finds local pathologies in the color gamuts of subtractive and complex‐subtractive colorant systems. These applications should be useful for the design of color atlases.