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.
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Acknowledgment
We thank Ethan Berkove, Hannah Gordon, Liz McMahon, and Steven Weintraub for useful comments on earlier drafts of this note.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
Gary Gordon
GARY GORDON received his BA from the University of Florida in 1977 and his Ph.D. from the University of North Carolina in 1983. He has taught math at Lafayette College since 1986. His mathematical interests include combinatorics, geometry, algebra, and all sorts of problem solving. His favorite mathematical project was writing the book The Joy of SET, about the math behind the card game SET, with his wife, Liz McMahon, and their two daughters Rebecca, and Hannah Gordon. He loves rock climbing, biking, and playing softball, tennis, golf and other sports where people swing clubs. He also spends way too much time watching baseball.