  Principal Component Analysis and biplots are so well-established and readily
implemented that it is just too tempting to give for granted their internal
workings. In this note I get back to basics in comparing how PCA and biplots
are implemented in base-R and contributed R packages, leveraging an
implementation-agnostic understanding of the computational structure of each
technique. I do so with a view to illustrating discrepancies that users might
find elusive, as these arise from seemingly innocuous computational choices
made under the hood. The proposed evaluation grid elevates aspects that are
usually disregarded, including relationships that should hold if the
computational rationale underpinning each technique is followed correctly.
Strikingly, what is expected from these equivalences rarely follows without
caveats from the output of specific implementations alone.
