Matrix Groups for Undergraduates

Kristopher Tapp, Saint Joseph's University, Philadelphia, PA, USA.

• Why study matrix groups?MatricesAll matrix groups are real matrix groupsThe orthogonal groupsThe topology of matrix groupsLie algebrasMatrix exponentiationMatrix groups are manifoldsThe Lie bracketMaximal toriHomogeneous manifoldsRootsBibliographyIndex

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