Pc correlation loadings extracted from a covariance matrix

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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) ^chas latent roots L^c and latent vectors P.

Reference no: EM131059941

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