AbstractWhen using hyphenated methods in analytical chemistry, the data obtained for each sample are given as a matrix. When a regression equation is set up between an unknown sample (a matrix) and a calibration set (a stack of matrices), the residual is a matrixR.The regression equation is usually solved by minimizing the sum of squares ofR. If the sample contains some constituent not calibrated for, this approach is not valid. In this paper an algorithm is presented which partitionsRinto one matrix of low rank corresponding to the unknown constituents, and one random noise matrix to which the least squares restrictions are applied. Properties and possible applications of the algorithm are also discussed.In Part 2 of this work an example from HPLC with diode array detection is presented and the results are compared with generalized rank annihilation factor analysis (GRAFA).