Matrix Algebra

Abstract

Many people regard journal articles and books that contain matrix algebra as prohibitively complicated and ignore them or shelve them indefinitely. This is a sad state of affairs because learning matrix algebra is not difficult and can reap enormous benefits. Science in general, and genetics in particular, is becoming increasingly quantitative. Matrix algebra provides a very economical language to describe our data and our models; it is essential for understanding LISREL and other data analysis packages. In common with most languages, the way to make it “stick” is to use it. Those unfamiliar with, or out of practice at, using matrices will benefit from doing the worked examples in the text. Readers with a strong mathematics background may skim this chapter, or skip it entirely, using it for reference only. We do not give an exhaustive treatment of matrix algebra and operations but limit ourselves to the bare essentials needed for structural equation modeling. There are many excellent texts for those wishing to extend their knowledge; we recommend Searle (1982) and Graybill (1969).