. . . uppJïp\ Jz(UpkJXk)2 = ip U;iA) 2 = A . . . UjpJXp )2 = Jïp

This equation shows that, when the eigenvectors are scaled to the lengths of their respective standard deviations JXk, the lengths of the descriptor-axes are Js2 = Sj (i.e. their standard deviations) in multidimensional space. The product of two descriptor-axes, which corresponds to their angle in the multidimensional space, is therefore equal to their covariance Sji.

* In some computer packages, the principal component procedure only scales the eigenvectors to length JX and only provides a plot of the descriptor-axes (no plot of the objects is available).

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