Chromatic adaptation transforms generally rely on a variant of the von Kries transformation-method to account for changes in the LMS cone signals that occur when changing from one illuminant to another. Von Kries adaptation also often referred to as the coefficient rule method or the diagonal transformation method-adjusts the 3 color channels by independent scale factors. Since there generally are only 3 known quantities available, namely the ratio of the cone signals of the two adapting illuminants, a crucial aspect of the von Kries method is that it requires only 3 parameters to be specified. A 9-parameter, 3x3 matrix transformation would be more accurate, but it is generally not possible to determine the extra parameters. This paper presents a novel method of predicting the effect a change of illumination has on the cone signals, while still relying on only 3 parameters. To begin, we create a large set of 3x3 matrices representing illuminant changes based on a sizable database of typical illuminant spectra and surface spectral reflectances. Representing these 3x3 matrices as points in a 9-dimensional space, we then apply principal components analysis to find a 3-dimensional basis which best approximates the original matrix space. To model an illumination change, a 3x3 matrix is constructed using a weighted combination of the 3 basis matrices. The relative weights can be calculated based on the 3 standard cone ratios obtained from the illuminant pair. Tests show that the new method yields better results than von Kries adaptation with or without sensor sharpening.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.