Matrix Groups for Undergraduates

Front Cover
American Mathematical Soc., 2005 - Mathematics - 166 pages
Matrix groups are a beautiful subject and are central to many fields in mathematics and physics. They touch upon an enormous spectrum within the mathematical arena. This textbook brings them into the undergraduate curriculum. It is excellent for a one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori. The volume is suitable for graduate students and researchers interested in group theory.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Why study matrix groups?
1
Chapter 1 Matrices
5
Chapter 2 All matrix groups are real matrix groups
23
Chapter 3 The orthogonal groups
33
Chapter 4 The topology of matrix groups
51
Chapter 5 Lie algebras
67
Chapter 6 Matrix exponentiation
79
Chapter 7 Matrix groups are manifolds
93
Chapter 8 The Lie bracket
113
Chapter 9 Maximal tori
135
Bibliography
163
Index
165
Back Cover
169
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information