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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Randall Eubank, Tailen Hsing

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Chapter 9Principal components analysis

In Section 1.1, we considered a c09-math-001-dimensional random vector c09-math-002 with c09-math-003 and covariance matrix c09-math-004. If

equation

is the eigenvalue–eigenvector decomposition for the covariance matrix, we saw that c09-math-005 could be decomposed as

equation

for c09-math-006 zero mean, uncorrelated random variables having c09-math-007. The c09-math-008 provide a new set of variables that are called the principal components of c09-math-009. One may, for example, ...

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