We apply the matrix representation technique to determine the concentrations of three dye components in the liquid‐crystal mixture needed to make a black‐and‐white guest‐host display. This method employs the Newton‐Raphson iterative process to match the tristimulus values of the mixture to the tristimulus values of the achromatic color. The color matches are thus metameric rather than spectral and hence depend upon the illuminant type. We give examples which show that practically any yellow, red, and blue dye components can be mixed to obtain a neutral color for a given illuminant, but that such mixtures generally have some coloration when viewed under other illuminant types. By extending the matrix representation technique into six dimensions, we show that it is possible to select optimum dye components according to the width and centroid wavelength of their absorption curves. These optimized components minimize the sensitivity of the neutral color to changes in illuminant type. We demonstrate that displays can be made with three optimized dye components which are achromatic under the extremes of both daylight and incandescent illumination. The absorption bands of these optimized dye components must be about 100 nm wide or wider, and the centroids of their respective absorption curves must be located within the ranges 445±10, 540±10, and 650±10 nm. We find that Heilmeier‐ and White‐and‐Taylor‐type displays generally require different dye formulations. Examples are given for both display types.