Principal components can be defined as those directions in data space that are stationary with regard to the variance. This definition is of course incomplete -- the missing part is the requirement that the directions have somehow ``normalized'' coefficients. In this talk, we will discuss the nature of this normalization: is it an arbitrary convention, or is there a necessity in certain choices of normalization? To answer this question, I propose that the normalizing quadratic form is also a variance, but calculated under a suitable null assumption. This ``null principle'' opens the door for a number of generalizations, such as the incorporation of smoothing splines and other penalty methods into conventional multivariate analysis. In the end, from this viewpoint we will be able to sort out some confusions in functional data analysis.