ABSTRACT
Inverse least-squares (ILS), sometimes known as P-matrix calibration, is so called because, originally, it involved the application of multiple linear regression to the inverse expression of the Beer-Lambert Law of spectroscopy: C= PA. To produce a calibration using inverse least-squares, the chapter deals with a training set consisting of a concentration matrix, C, and an absorbance matrix, A, for known calibration samples. it seeks to solve for the calibration or regression matrix, P. P contains the calibration, or regression, coefficients which are used to predict the concentrations of an unknown from its spectrum. P will contain one row of coefficients for each component being predicted. It is important to note that there are many publications which discuss optimal ways of selecting individual spectral wavelengths for use with ILS. Much of this work comes from the near infrared community.
