Principal Component Analysis pp 8-22 | Cite as

# Mathematical and Statistical Properties of Population Principal Components

## Abstract

In this chapter many of the mathematical and statistical properties of PCs are described, based on a known population covariance (or correlation) matrix **Σ**. Further properties are included in Chapter 3 but in the context of sample, rather than population, PCs. As well as being derived from a statistical viewpoint, PCs can be found using purely mathematical arguments; they are given by an orthogonal linear transformation of a set of variables which optimizes a certain algebraic criterion. In fact, the PCs optimize several different algebraic criteria and these optimization properties, together with their statistical implications, are described in the first section of the chapter.

## Keywords

Covariance Matrix Covariance Matrice Correlation Matrice Generalize Varianee Constant Probability## Preview

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