The standard color space conversion equations usually do not explicitly account for a change in luminance. In an effort to understand color space conversion better, the color space conversion equations are derived from first principles. The solution shows how to calculate the RGB scale factors using xyY measured at a RGB triplet that is not restricted to white. Also, the color space conversion equations are discussed in the context of color encoding topics including gamma, luminance, and negative primary settings.
David A. LeHoty, David A. LeHoty,
"Normalization factors in color space conversion", Proc. SPIE 6807, Color Imaging XIII: Processing, Hardcopy, and Applications, 68070G (28 January 2008); doi: 10.1117/12.775562; https://doi.org/10.1117/12.775562