Grassmann's laws let color matching be decomposed into independent primary matches then summed

Grassmann’s empirical laws state that color matching is linear: if light A matches B, and C matches D, then A+C matches B+D. This means a complex color can be matched by separately matching each primary component and summing the results. It is the foundation of all matrix-based color space conversions: match pure R, pure G, and pure B primaries separately; combine with superposition. Breaks down only in edge cases (very large visual fields or simultaneous contrast effects).

Examples

To derive the RGB→RGB matrix, match pure R, G, and B independently to get three equation sets; combine them. The resulting coefficients are the matrix columns.

Assessment

Explain in one sentence why you can match three color space primaries separately and combine the results, rather than matching every possible color individually.