  These notes have been adapted from an undergraduate course given by Professor
Alan James at the University of Adelaide from around 1965 and onwards. This
adaption has put a focus on the definition of projection matrices and the sweep
operator. These devices were at the heart of the development of the statistical
package Genstat which initially focussed on the analysis of variance using the
sweep operator. The notes provide an algebraic background to the sweep operator
which has since been used to effect in a number of experimental design
settings.
