Projection matrices and the sweep operator

TL;DR

This paper provides an algebraic overview of projection matrices and the sweep operator, highlighting their historical development and application in statistical analysis and experimental design.

Contribution

It offers a detailed algebraic explanation of the projection matrices and sweep operator, emphasizing their role in the development of statistical methods and software.

Findings

Historical context of the sweep operator

Application in analysis of variance

Foundation for statistical software Genstat

Abstract

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.