A note on rank deficiency and numerical modeling

Linearly dependent concentration profiles of a chemical reaction can result in a spectral data matrix with a chemical rank smaller than the number of absorbing chemical species. Such a rank deficiency is problematic for a factor analysis as some information on the pure component spectra cannot be recovered from the mixture data. Matrix augmentation can break rank deficiencies and enable successful pure component recovery. In contrast to this, an artificial breakdown of a rank deficiency can be caused by a numerical finite precision simulation of the underlying kinetic model and can fake a successful MCR analysis. This work discusses the problem and points out some remedies. Linearly dependent concentration profiles of a chemical reaction can result in a spectral data matrix with a chemical rank smaller than the number of absorbing chemical species. This work discusses such rank deficiencies and the artificial breakdown of a rank deficiency by a finite precision numerical simulation.