Overview
Emphasizes the interplay between algebra and geometry
Accessible to advanced undergraduates/graduate students, in a variety of subject areas, including mathematics, physics, engineering, and computer science
Useful reference material for mathematicians and professionals
Contains numerous practice problems at the end of each section
Includes supplementary material: sn.pub/extras
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group.
Applications involving symm
etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.Reviews
“It is particularly applicable for anyone who is familiar with vector spaces and wants to learn about groups – and also for anyone who is familiar with groups and wants to learn about vector spaces. This book is well readable and therefore suitable for self-studying. Each chapter begins with a concise and informative summary of its content, guiding the reader to choose the chapters with most interest to him/her.” (Jorma K. Merikoski, zbMATH 1380.15001, 2018)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Groups, Matrices, and Vector Spaces
Book Subtitle: A Group Theoretic Approach to Linear Algebra
Authors: James B. Carrell
DOI: https://doi.org/10.1007/978-0-387-79428-0
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media LLC 2017
Hardcover ISBN: 978-0-387-79427-3Published: 03 September 2017
Softcover ISBN: 978-1-4939-7910-3Published: 03 August 2018
eBook ISBN: 978-0-387-79428-0Published: 02 September 2017
Edition Number: 1
Number of Pages: XVII, 410
Topics: Commutative Rings and Algebras, Linear and Multilinear Algebras, Matrix Theory, Group Theory and Generalizations, Algebraic Geometry