Can You Use Principal Component Analysis with a Training Set Test Set Model?

I recently gave a free webinar on Principal Component Analysis. We had almost 300 researchers attend and didn't get through all the questions. This is part of a series of answers to those questions. If you missed it, you can get the webinar recording here. Principal Component Analysis specifically could be used with a training and test data set, but it doesn't make as much sense as doing so for Factor Analysis.