Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent 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 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.
Rezensionen / Stimmen
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 fuer 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
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Editions-Typ
Maße
Höhe: 203 mm
Breite: 140 mm
Gewicht
ISBN-13
978-1-4704-2722-1 (9781470427221)
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Schweitzer Klassifikation
Kristopher Tapp, Saint Joseph's University, Philadelphia, PA, USA.
Why study matrix groups?
Matrices
All matrix groups are real matrix groups
The orthogonal groups
The topology of matrix groups
Lie algebras
Matrix exponentiation
Matrix groups are manifolds
The Lie bracket
Maximal tori
Homogeneous manifolds
Roots
Bibliography
Index
