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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010201076 | QA184.2 T37 2005 | Open Access Book | Book | Searching... |
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Summary
Summary
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 basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.
Reviews 1
Choice Review
This text is a fairly in-depth introduction to matrix groups. Tapp (Saint Joseph's Univ.) utilizes the premise of studying the symmetries of a sphere to introduce readers to the linear, orthogonal, unitary, and symplectic groups. As a result of this premise, it is possible to perform and see the underlying geometry as the groups are developed. One highlight of this text is the consideration of these matrix groups over Hamilton's skew field (or quaternions), as few undergraduate presentations of matrix groups include more than the real numbers and seldom discuss the role complex numbers play in such groups. By doing so, Tapp is easily able to transition into a comprehensible introduction to Lie algebras and Lie groups. In addition, by focusing on the symmetries of a sphere, the topology of matrix groups is also accessible, including maximal tori and manifolds. With the prerequisites of multivariable calculus, linear algebra, and a little abstract algebra, readers are exposed to the basics behind the multitude of matrix group applications and finish with a desire to learn more. Summing Up: Recommended. Upper-division undergraduates through researchers and faculty. --John T. Zerger, Catawba College
Table of Contents
| 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 |
| Bibliography |
| Index |
