Matrices and Galois Theory

Abstract

Summary This note shows how to use matrix operations to solve problems students encounter in Galois theory. In particular, we show how eigenspaces can be used to find fixed fields for automorphisms. We illustrate the methods with an example, and we also give a brief description of the general procedure. Adding this approach to a standard course in Galois theory allows students to see another example of how linear algebra appears naturally in more advanced courses.