**Student Mathematical Library**

Volume: 29;
2005;
166 pp;

MSC: Primary 20;
Secondary 22

**Electronic ISBN: 978-1-4704-2140-3
Product Code: STML/29.E**

List Price: $34.00

Individual Price: $27.20

#### Supplemental Materials

# Matrix Groups for Undergraduates

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*Kristopher Tapp*

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.

#### Table of Contents

# Table of Contents

## Matrix Groups for Undergraduates

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Why study matrix groups? 18 free
- Chapter 1. Matrices 512
- Chapter 2. All matrix groups are real matrix groups 2330
- Chapter 3. The orthogonal groups 3340
- §1. The standard inner product on K[sup(n)] 3340
- §2. Several characterizations of the orthogonal groups 3643
- §3. The special orthogonal groups 3946
- §4. Low dimensional orthogonal groups 4047
- §5. Orthogonal matrices and isometries 4148
- §6. The isometry group of Euclidean space 4350
- §7. Symmetry groups 4552
- §8. Exercises 4754

- Chapter 4. The topology of matrix groups 5158
- Chapter 5. Lie algebras 6774
- Chapter 6. Matrix exponentiation 7986
- Chapter 7. Matrix groups are manifolds 93100
- Chapter 8. The Lie bracket 113120
- Chapter 9. Maximal tori 135142
- §1. Several characterizations of a torus 136143
- §2. The standard maximal torus and center of SO(n), SU(n), U(n) and Sp(n) 140147
- §3. Conjugates of a maximal torus 145152
- §4. The Lie algebra of a maximal torus 152159
- §5. The shape of SO(3) 154161
- §6. The rank of a compact matrix group 155162
- §7. Who commutes with whom? 157164
- §8. The classification of compact matrix groups 158165
- §9. Lie groups 159166
- §10. Exercises 160167

- Bibliography 163170
- Index 165172
- Back Cover Back Cover1176