¥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
¥The results presented may have aTkak = 1, but alternatives are aTkak = λk or aTkak = 1/ λk, where λk is the
eigenvalue (variance) associated with the kth PC
¥In interpreting what a PC represents in terms
of the original variables, the normalisation is unimportant – the maps look exactly the same. It is the relative values of the akj within ak that are important.
¥However, there are differences in
interpretation of individual loadings which need not concern us here