  Data matrix centering is an ever-present yet under-examined aspect of data
analysis. Functional data analysis (FDA) often operates with a default of
centering such that the vectors in one dimension have mean zero. We find that
centering along the other dimension identifies a novel useful mode of variation
beyond those familiar in FDA. We explore ambiguities in both matrix orientation
and nomenclature. Differences between centerings and their potential
interaction can be easily misunderstood. We propose a unified framework and new
terminology for centering operations. We clearly demonstrate the intuition
behind and consequences of each centering choice with informative graphics. We
also propose a new direction energy hypothesis test as part of a series of
diagnostics for determining which choice of centering is best for a data set.
We explore the application of these diagnostics in several FDA settings.
