Data matrices consisting of sample optical absorption as a function of wavelength and another variable, such as time, are decomposable using known matrix algebraic methods. The natural decomposition, based on the Beer-Lambert law, into the product of component absorbance and (time dependent) concentration matrices is usually not straightforward. Singular value decomposition yields orthonormal spectral and kinetic eigenvectors, with mathematical but not physical meaning. The connection of the two decompositions is explored with reference to the problem of the bacteriorhodopsin photocycle. The limitations and applicability of singular value decomposition with self-modeling is evaluated with known stoichiometric constraints on the intermediate kinetics and compared to other techniques applied to the same problem. The improved method of exponential fit assisted self-modeling is introduced and demonstrated on realistic simulated data.