Groups, Matrices, and Vector Spaces

A Group Theoretic Approach to Linear Algebra

Authors: Carrell, James B.

  • 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
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Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-0-387-79428-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-0-387-79427-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

James B. Carrell is Professor Emeritus of mathematics at  the University of British Columbia. His research areas include algebraic transformation groups, algebraic geometry, and Lie theory.

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Table of contents (12 chapters)

  • Preliminaries

    Carrell, James B.

    Pages 1-9

  • Groups and Fields: The Two Fundamental Notions of Algebra

    Carrell, James B.

    Pages 11-55

  • Matrices

    Carrell, James B.

    Pages 57-83

  • Matrix Inverses, Matrix Groups and the $${ LPDU}$$ Decomposition

    Carrell, James B.

    Pages 85-111

  • An Introduction to the Theory of Determinants

    Carrell, James B.

    Pages 113-134

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-0-387-79428-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-0-387-79427-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Groups, Matrices, and Vector Spaces
Book Subtitle
A Group Theoretic Approach to Linear Algebra
Authors
Copyright
2017
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media LLC
eBook ISBN
978-0-387-79428-0
DOI
10.1007/978-0-387-79428-0
Hardcover ISBN
978-0-387-79427-3
Edition Number
1
Number of Pages
XV, 410
Topics