@Sycorax: That is actually a "pretty old" and well-known introductory paper - I remember reading it quite a few times. I don't know why it was added in arxiv in 2014 but versions of it are around since 2003. (eg. cs.princeton.edu/picasso/mats/PCA-Tutorial-Intuition_jp.pdf)

@whuber: I would say it is a useful and well-written paper especially for people not from a Maths/Stats educational background. I have given it to juniors analysts in my work as a second read and working it through it has been a good exercise for them. Yes, as all papers it needs a clarification here and there, but it is not supposed to replace Jolliffe's PCA book. :)