Let be a centered and scaled data matrix that has *k* numerical variables. The eigenvalue decomposition method bases the component extraction on the eigenvalue decomposition of
the covariance matrix , which extracts all the *k* principal components simultaneously. Each principal component is a linear combination of the original variables, and each
component is orthogonal, with coefficients equal to the eigenvectors of the covariance matrix . The eigenvectors are usually normalized to have unit length. The principal components are sorted by descending order of
the eigenvalues, which are equal to the variances of the components.