The determination of the number of species present in a system: A new matrix rank treatment of spectrophotometric data

Abstract

A method is described for the determination of the number of independent variables (e.g., number of different species) in a chemical system. For the application of the method one measures a set of properties Pij (such as absorbances at different wavelengths) in several different mixtures, with the requirement that Pij = ΣkPikCkj. These are then arranged in a rectangular matrix and the number of independent variables is determined from the rank of the matrix, obtained by finding the number of nonzero eigenvalues. In addition, a statistical criterion for the vanishing of an eigenvalue is proposed.