Euclidean Color Space and Its Invariants.

Color mixture is not mixture of color sensations, as taught by Young and Maxwell, but the processing of (alpha) proximal color stimuli to other (beta) proximal color stimuli and then color sensations occur. The processing is described by linear algebraic mapping. Color theorists (Schrodinger and others) have insisted that beta color stimuli are described only by affine geometry where distance and angle are without meaning. This reflected views of older geometers holding that affine geometry was Euclidean geometry stripped of all postulates and axioms concerning distance and angle. Modern linear algebraists, however, hold the obverse view, that a Euclidean metric is inherent in any affine space. Euclidean color space is proved and demonstrated by the invariant symmetrical matrix of scalar products between spectral vectors; this identical matrix may be derived from any set of affine color mixture functions. The invariant matrix may be resolved to an infinite number of Euclidean color mixture functions; each is a three-column matrix showing projections of spectral vectors onto oblique or orthogonal axes. Beta color vector length is luminous power, a new construct shown to predict the efficiency of color stimuli in color mixture. One preferred oblique reference frame (one achromatic axis and two axes on an orthogonal chromatic plane) are described. Color mixture is predicted by vector addition analogous to the vector addition of forces in mechanics. No assumptions have been used beyond those embodied in color mixture data.