Choosing the Right Type of Rotation in PCA and EFA

Question: In Chapter 7 of the 2008 book on heritage language learning that you co-edited with Kimi Kondo-Brown, there is a study (Lee & Kim, 2008) comparing the attitudes of 111 Korean heritage language learners. On page 167 of that book, a principal components analysis (with varimax rotation) describes the relation of examining 16 purported reasons for studying Korean with four broader factors. Several questions come to mind. What is a principal components analysis? How does principal components analysis differ from factor analysis? What guidelines do researchers need to bear in mind when selecting “factors”? And finally, what is a varimax rotation and why is it applied?