Principal Component Analysis (page 4 of 5)

Eigenvectors and eigenvalues always come in pairs, which means that every eigenvector has a corresponding eigenvalue. These eigenvectors and eigenvalues determine the directions of the PCA axes. That is, the eigenvectors of the Covariance matrix are the directions of the axes where there is the most variance and most information, which represent the different princiapl components. Furthermore, eigenvalues are the coefficients attached to eigenvectors. By ranking your eigenvectors in order of their eigenvalues (highest to lowest), we get the principal components in order of importance.