As we stated above, we start factor analysis with principal component analysis, but we quickly diverge as we apply the a priori knowledge we brought to the problem.

This knowledge may be of the form that we "know" how inany factors there should be or it may be more of the nature that allows our experience and intuition about the data guide us as to how many factors there should be. As before, with PCA, we can take the eigenvectors (of unit length) and weight them with the square root of the corresponding eigenvalue: