As PCA and PLS are basic tools for every chemometrician, the recent article with comprehensive reasoning of mathematical complexities of dependences between them  is a very good lecture for curious researchers.
- J.L. Godoy, J.R. Vega, and J.L. Marchetti, "Relationships between PCA and PLS-regression", Chemometrics and Intelligent Laboratory Systems, vol. 130, pp. 182-191, 2014. http://dx.doi.org/10.1016/j.chemolab.2013.11.008