Generalized rank annihilation method using similarity transformations

Recently several papers have described the generalized rank annihilation method; however, in some cases complex eigenvalues and eigenvectors may appear when the generalized eigenproblem is solved. When complex eigenvalues and eigenvectors are encountered, the results cannot be used to estimate pure component profiles (e.g. spectra or chromatograms). In this paper, a similarity transformation is used to transform complex eigenvalues and eigenvectors into real eigenvalues and eigenvectors, thereby permitting spectra and profiles of pure constituents to be estimated. The modified GRAM method is illustrated with simulated and real data.