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Using Eq. (3.103a and b) prove the results of Theorem 3.17.
THEOREM 3.17
(Singular Value Decomposition) Let X be a (n x p) data matrix such that p(X) = p ≤n, = 0, and let XTX and XXT be (p x p) and (n x n) Grammian matrices respectively, Then
(i) Nonzero latent vectors of XXT are standardized PCs of XTX.
(ii) Nonzero latent roots of XTX and XXT rare equal.
(iii) Any real (n x p) matrix X can be decomposed as
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