Dimensional analysis
Principal compenent analysis (PCA)

There are two function in the basics stats package prcomp() and princomp() and three functions in packages from the French school of data analysis PCA() {FactoMineR} dudi.pca() {ade4} and acp() {amap}.

You will have to look up the documentation for the details, below you will only find some examples for the most common tasks.

princomp (prcomp) performs a principal components analysis on a numeric data matrix and returns the results as an object of class princomp (prcomp).

Plotting loadings and scores

A nicer plot for the scores (using {ggplot2}

A simple loadings plot with labels (using base graphics); plots by default the first two components

Other factor analytical and dimensional techniques

Note this section is very sketchy; there is a lot more in the R Universe