Zero Order Design: Generalized Inverses, Adjustment, the Datum Problem and S-Transformations

Many problems in physical science involve the estimation of a number of unknown parameters which bear a linear (or linearized) relationship to a set of experimental data. The data may be contaminated by (systematic or random) errors, insufficient to determine the unknowns, redundant, or all of the above and consequently, questions as existence, uniqueness, stability, approximation and the physical description of the set of solutions are all of interest.