  Principal Component Analysis (PCA) is a highly useful topic within an
introductory Linear Algebra course, especially since it can be used to
incorporate a number of applied projects. This method represents an essential
application and extension of the Spectral Theorem and is commonly used within a
variety of fields, including statistics, neuroscience, and image compression.
We present a synopsis of PCA and include a number of examples that can be used
within upper-level mathematics courses to engage undergraduate students while
introducing them to one of the most widely-used applications of linear algebra.
