When Principal Components Analysis and Factor Analysis identify the underlying factors they do so using a greedy algorithm. They begin by identifying the first component in such a way that it explains as much variance as possible, and proceed by identifying the next component in such a way that it explains the maximum possible amount of the remaining variance and so on.
The solution identified by the greedy algorithm is one of an infinite number of possible solutions that are identifiable in terms of the total amount of variance they explain. For example, if five components are identified, there are an infinite number of different five component solutions, each of which explain the same variance as the solution identified by the greedy algorithm. In a purely mathematical sense, each of these possible solutions is identical. However, the solutions can differ greatly in terms of how easy they are to interpret.
Varimax rotation is a way of transforming the solution so that Rotated Component Matrix is relatively easy to understand. In particular, it identifies a solution where, to the maximum extent possible, correlations in the rotated component matrix are close to 1, -1 or 0..
Almost all applications of principal components analysis and factor analysis in survey research apply the Varimax Rotation.
- Kaiser, H. F. (1958). "The Varimax Criterion for Analytic Rotation in Factor Analysis." Psychometrika 23(3 September): 187-200.