¥If x is a vector of p variables, then the principal components (PCs) are linear
combinations aT1x, aT2x, É aTpx
¥Although we can find p PCs, and sometimes the last few are useful (e.g in finding
outliers), for dimension reduction purposes we usually only
keep the first few
¥In the kth PC ak, the vector of coefficients or loadings, is chosen so that the variance
of aTkx is maximised,
subject to a normalisation constraint aTkak = 1, and
subject to successive PCs being
uncorrelated
¥