Tensorial calibration: I. First‐order calibration

Abstract Many analytical instruments now produce one‐, two‐ or n ‐dimensional arrays of data that must be used for the analysis of samples. An integrated approach to linear calibration of such instruments is presented from a tensorial point of view. The data produced by these instruments are seen as the components of a first‐, second‐ or n th‐order tensor respectively. In this first paper, concepts of linear multivariate calibration are developed in the framework of first‐order tensors, and it is shown that the problem of calibration is equivalent to finding the contravariant vector corresponding to the analyte being calibrated. A model of the subspace spanned by the variance in the calibration must be built to compute the contravarian vectors. It is shown that the only difference between methods such as least squares, principal components regression, latent root regression, ridge regression and partial least squres resides in the choice of the model.