ABSTRACT
This chapter describes the operations, and then considers the correspondence between vectors and variables. A geometric vector gives a concrete representation to a variable and to the algebraic vector of data that measures it. Before applying this geometric representation to the techniques of multivariate statistics, one needs to understand how to manipulate these vectors and combine them. The single vector has only its length, the two vectors have the area just described, and the three vectors set out a volume. These three concepts are analogous in their respective spaces, and it is helpful to have a general notation that encompasses them and allows for more than three vectors. Another operation of importance to the geometry of multivariate statistics is the rotation of a set of vectors. The geometry of rotation is quite straightforward. It concludes by describing the important concepts of vector spaces, linear dependence, and projection.
