In PCA multicollinearity is not a problem as matrix inversion is not required, yet for most forms of FA singularity and multicollinearity is a problem. If the determinant of R and eigenvalues associated with some factors approach zero, multicollinearity or singularity may be present. Deletion of singular or multicollinear variables is required. Transformation of data through rewriting the data with properties the original data did not have. The data may be efficiently simplified prior to a classification while also removing artifacts such as multicollinearity.
Loadings relate the specific association between factors and original variables.
Therefore, it is necessary to find the loadings, then solve for the factors, which will approximate the relationship between the original variables and underlying factors. The loadings are derived from the magnitude of eigenvalues associated to individual variables. The level of unique variance is dictated by the FA model which is chosen. Accordingly, PCA is a model of a closed system, while FA is a model of an open system. Rotation attempts to put the factors in a simpler position with respect to the original variables, which aids in the interpretation of factors.