The use of linear algebra and set theoretic estimation for problems in color science and imaging is reviewed. Through a product-space formalism, the powerful projection onto convex sets (POCS) algorithm is extended to subtractive color systems satisfying convex constraints in the density domain. Several convex sets are defined, which are useful in color science and imaging, and projections onto these sets are presented. The usefulness of the new methods is demonstrated by applying them to three practical problems; (1) model-based scanner calibration, (2) design of color scanning filters that are color mixture curve, and (3) colorant formulation.