Using Theorem 3.15 show that PC correlation loadings extracted from a covariance matrix are identical to those from a correlation matrix if the variances of the variables are equal

THEOREM 3.15

Let X be a (n x p) data matrix such that ₁= ₂= • • • = _p =0, and where X^TX has latent roots L and latent vectors P. Then for some scalar c,

(i) cX^TX has latent roots cL and latent vectors P.

(ii) X^TX + cl has latent roots L + cI and latent vectors P.

(iii) (X^TX) ^c has latent roots L^c and latent vectors P.