Explanation
PCA is a statistical tool that decomposes a positive semi-definite matrix into its principal components. The first few principal components explain nearly all the variation and other components can then be ignored as they are too small in the larger picture. PCA in risk management is applied to a positive semi-definite correlation or covariance matrix to reveal the principal components that cause the variation. By allowing a focus on a few components, PCA reduces dimensionality.
While performing the math of PCA is unlikely to be asked in the PRMIA exam, you should remember that principal components have the additional property of being uncorrelated to each other which makes it useful as it is possible to vary one of the components without having to worry about the effect of that on the other components.