There is a second approach to the study of the relationships among descriptors. It consists in scaling the eigenvectors in such a way that the cosines of the angles between descriptor-axes be proportional to their covariances. In this approach, the angles between descriptor-axes are between 0° (maximum positive covariance) and 180° (maximum negative covariance); an angle of 90° indicates a null covariance (orthogonality). This result is achieved by scaling each eigenvector k to a length equal to its standard deviation JXk . Using this scaling for the eigenvectors, the Euclidean distances among objects are not preserved.
Using the diagonal matrix A of eigenvalues (eq. 2.20), the new matrix of eigenvectors can be directly computed by means of expression UA1/2. For the numerical example:
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