Mathematical and Statistical Properties of Population Principal Components

  • I. T. Jolliffe
Part of the Springer Series in Statistics book series (SSS)


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.


Covariance Matrix Covariance Matrice Correlation Matrice Generalize Varianee Constant Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • I. T. Jolliffe
    • 1
  1. 1.Mathematical InstituteUniversity of KentKentEngland

Personalised recommendations