Review of Vector and Matrix Algebra

In this chapter, we introduce basic results dealing with vector spaces and matrices, which are essential for an understanding of linear statistical methods. We provide several numerical and geometrical illustrations of these concepts. The material presented in this chapter will be found in most textbooks that deal with matrix theory pertaining to linear models, including Graybill (1983), Harville (1997), Rao (1973a), and Searle (1982). Unless stated otherwise, all vectors and matrices are assumed to be real, i.e., they have real numbers as elements.