Linear algebra is the workhorse of modern data science and machine learning, but none of the fun applications are ever mentioned in Math 18. We remedy this by discussing Principal Component Analysis,,the best* of these applications, and show how it follows quickly from the Singular Value Decomposition, the best* theorem in linear algebra. We present a few mathematical perspectives, explain the equivalent formulations of PCA, and ultimately use PCA to build an elementary image classifier without any fancy tools from machine learning.

^{*The speaker does not necessarily believe any of these claims but will nonetheless defend them vehemently if heckled.}