Softcover ISBN:  9781470427221 
Product Code:  STML/79 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470429386 
Product Code:  STML/79.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9781470427221 
eBook: ISBN:  9781470429386 
Product Code:  STML/79.B 
List Price:  $108.00 $83.50 
Softcover ISBN:  9781470427221 
Product Code:  STML/79 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470429386 
Product Code:  STML/79.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9781470427221 
eBook ISBN:  9781470429386 
Product Code:  STML/79.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 79; 2016; 239 ppMSC: Primary 20; Secondary 22
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent 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 the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots.
This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.
From reviews of the First Edition:
This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. ... The book combines an intuitive style of writing with rigorous definitions and proofs, giving examples from fields of mathematics, physics, and other sciences where matrices are successfully applied. The book will surely be interesting and helpful for students in algebra and their teachers.
—European Mathematical Society Newsletters
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 one semester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses.
—MathSciNet (or Mathematical Reviews)
ReadershipUndergraduate and graduate students and research mathematicians interested in teaching and learning Lie groups, in particular, classical Lie groups.

Table of Contents

Chapters

Chapter 1. Why study matrix groups?

Chapter 2. Matrices

Chapter 3. All matrix groups are real matrix groups

Chapter 4. The orthogonal groups

Chapter 5. The topology of matrix groups

Chapter 6. Lie algebras

Chapter 7. Matrix exponentiation

Chapter 8. Matrix groups are manifolds

Chapter 9. The Lie bracket

Chapter 10. Maximal tori

Chapter 11. Homogeneous manifolds

Chapter 12. Roots


Additional Material

Reviews

This book offers a very nice introduction to the theory of matrix groups and their Lie algebras. The background is kept to a minimum, only basics of calculus, linear algebra and group theory are assumed, while background on topology (of subsets of Euclidean space) is developed in the text. While the text gives complete and exact proofs, it is easy to read, appeals to intuition, and contains many pictures and helpful exercises.
A. Cap, Monatshefte für Mathematik 
[T]he second edition is an expanded and improved version of the original. It can be strongly recommended for an undergraduate course in Lie groups, or as complementary reading for a course in group theory. Prerequisites are basic: knowledge of algebra, geometry, and analysis at an undergraduate level. Hence the book is suitable for a wide audience of readers who are meeting applications of group theory in other areas of mathematics and physics, or even further afield.
Alla S. Detinko, Mathematical Reviews 
The author gives an inspiring presentation of the topics presented in this book.
Erich W. Ellers, Zentralblatt Math


RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent 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 the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots.
This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.
From reviews of the First Edition:
This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. ... The book combines an intuitive style of writing with rigorous definitions and proofs, giving examples from fields of mathematics, physics, and other sciences where matrices are successfully applied. The book will surely be interesting and helpful for students in algebra and their teachers.
—European Mathematical Society Newsletters
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 one semester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses.
—MathSciNet (or Mathematical Reviews)
Undergraduate and graduate students and research mathematicians interested in teaching and learning Lie groups, in particular, classical Lie groups.

Chapters

Chapter 1. Why study matrix groups?

Chapter 2. Matrices

Chapter 3. All matrix groups are real matrix groups

Chapter 4. The orthogonal groups

Chapter 5. The topology of matrix groups

Chapter 6. Lie algebras

Chapter 7. Matrix exponentiation

Chapter 8. Matrix groups are manifolds

Chapter 9. The Lie bracket

Chapter 10. Maximal tori

Chapter 11. Homogeneous manifolds

Chapter 12. Roots

This book offers a very nice introduction to the theory of matrix groups and their Lie algebras. The background is kept to a minimum, only basics of calculus, linear algebra and group theory are assumed, while background on topology (of subsets of Euclidean space) is developed in the text. While the text gives complete and exact proofs, it is easy to read, appeals to intuition, and contains many pictures and helpful exercises.
A. Cap, Monatshefte für Mathematik 
[T]he second edition is an expanded and improved version of the original. It can be strongly recommended for an undergraduate course in Lie groups, or as complementary reading for a course in group theory. Prerequisites are basic: knowledge of algebra, geometry, and analysis at an undergraduate level. Hence the book is suitable for a wide audience of readers who are meeting applications of group theory in other areas of mathematics and physics, or even further afield.
Alla S. Detinko, Mathematical Reviews 
The author gives an inspiring presentation of the topics presented in this book.
Erich W. Ellers, Zentralblatt Math