
Book DetailsStudent Mathematical LibraryVolume: 29; 2005; 166 ppMSC: Primary 20; Secondary 22
Now available in Second Edition: STML/79
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 onesemester 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 exampledriven, 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.
ReadershipUndergraduates and beginning graduate students interested in group theory.

Table of Contents

Chapters

Why study matrix groups?

Chapter 1. Matrices

Chapter 2. All matrix groups are real matrix groups

Chapter 3. The orthogonal groups

Chapter 4. The topology of matrix groups

Chapter 5. Lie algebras

Chapter 6. Matrix exponentiation

Chapter 7. Matrix groups are manifolds

Chapter 8. The Lie bracket

Chapter 9. Maximal tori


Additional Material

Reviews

this is an excellent, wellwritten textbook which is strongly recommended to a wide audience of readers interested in mathematics and its applications. The book is suitable for a onesemester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses.
Mathematical Reviews

 Book Details
 Table of Contents
 Additional Material
 Reviews
Now available in Second Edition: STML/79
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 onesemester 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 exampledriven, 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.
Undergraduates and beginning graduate students interested in group theory.

Chapters

Why study matrix groups?

Chapter 1. Matrices

Chapter 2. All matrix groups are real matrix groups

Chapter 3. The orthogonal groups

Chapter 4. The topology of matrix groups

Chapter 5. Lie algebras

Chapter 6. Matrix exponentiation

Chapter 7. Matrix groups are manifolds

Chapter 8. The Lie bracket

Chapter 9. Maximal tori

this is an excellent, wellwritten textbook which is strongly recommended to a wide audience of readers interested in mathematics and its applications. The book is suitable for a onesemester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses.
Mathematical Reviews