Mathematical and Statistical Properties of Sample Principal Components

Abstract

The first part of this chapter will be similar in structure to Chapter 2, except that it will deal with properties of PCs obtained from a sample covariance (or correlation) matrix, rather than from a population covariance (or correlation) matrix. The first two sections of the chapter, as in Chapter 2, describe respectively many of the algebraic and geometric properties of PCs. Most of the properties discussed in Chapter 2 are almost the same for samples as for populations, and will only be mentioned again briefly. There are, however, some additional properties which are relevant only to sample PCs and these will be discussed more fully.