Principal Component Analysis: Resources for an Essential Application of Linear Algebra

TL;DR

This paper provides an overview of Principal Component Analysis (PCA), highlighting its importance as an application of linear algebra, with examples suitable for teaching undergraduate students across various fields.

Contribution

It offers a comprehensive synopsis of PCA, connecting it to the Spectral Theorem and providing educational resources for incorporating PCA into advanced mathematics courses.

Findings

PCA is a key application of the Spectral Theorem.

Examples demonstrate PCA's relevance in statistics, neuroscience, and image compression.

Educational resources facilitate teaching PCA to undergraduates.

Abstract

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.