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.

[1]  Bruce R. Kowalski,et al.  Generalized rank annihilation factor analysis , 1986 .

[2]  G. Stewart,et al.  An Algorithm for Generalized Matrix Eigenvalue Problems. , 1973 .

[3]  Avraham Lorber,et al.  Features of quantifying chemical composition from two-dimensional data array by the rank annihilation factor analysis method , 1985 .

[4]  Bruce R. Kowalski,et al.  Generalized rank annihilation method , 1987 .

[5]  Bruce R. Kowalski,et al.  Generalized rank annihilation method : II. Analysis of bimodal chromatographic data , 1987 .

[6]  E. R. Malinowski,et al.  Rank Annihilation Factor Analysis of Unresolved LC Peaks , 1983 .

[7]  Linda B. McGown,et al.  Resolution of multicomponent fluorescent mixtures by analysis of the excitation–emission–frequency array , 1990 .

[8]  J. Callis,et al.  Multichannel imaging spectrophotometer for direct analysis of mixtures on thin-layer chromatography plates , 1983 .

[9]  D. Jenner,et al.  Determination of cortisol and cortisone in urine using high-performance liquid chromatography with UV detection. , 1985, Journal of pharmaceutical and biomedical analysis.

[10]  Avraham Lorber,et al.  Quantifying chemical composition from two-dimensional data arrays , 1984 .

[11]  Bruce R. Kowalski,et al.  The Generalized Standard Addition Method. , 1979 .

[12]  Bruce R. Kowalski,et al.  An improved algorithm for the generalized rank annihilation method , 1989 .

[13]  E. Davidson,et al.  Application of the method of rank annihilation to quantitative analyses of multicomponent fluorescence data from the video fluorometer , 1978 .

[14]  Avraham Lorber,et al.  Validation of hypothesis on a data matrix by target factor analysis , 1984 .

[15]  C. Shackleton,et al.  Use of Sep-pak cartridges for urinary steroid extraction: evaluation of the method for use prior to gas chromatographic analysis. , 1980, Clinica chimica acta; international journal of clinical chemistry.