Curve resolution of three-factor systems

Having derived a solution for two-component systems, we could try and extend this solution to three-component systems. A PCA of a data set of spectra of three-component mixtures yields three significant eigenvectors and a score matrix with three scores for each spectrum. Therefore, the spectra are located in a three-dimensional space defined by the eigenvectors. For the same reason, explained for the two-component system, by normalization, the ternary spectra are found on a surface with one dimension less than the number of compounds, in this case, a plane. 

If the ternary mixtures span the whole concentration range, i.e. from 0 to 100% for each component, some of the mixtures contains only one or two compounds. As explained before, the binary mixtures should be found on straight lines. In this 

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