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Linear Algebra Through Geometry

  • Thomas Banchoff
  • John Wermer

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Thomas Banchoff, John Wenner
    Pages 1-2
  3. Thomas Banchoff, John Wermer
    Pages 3-22
  4. Thomas Banchoff, John Wermer
    Pages 23-28
  5. Thomas Banchoff, John Wermer
    Pages 29-38
  6. Thomas Banchoff, John Wermer
    Pages 39-48
  7. Thomas Banchoff, John Wermer
    Pages 49-59
  8. Thomas Banchoff, John Wermer
    Pages 60-73
  9. Thomas Banchoff, John Wermer
    Pages 74-83
  10. Thomas Banchoff, John Wermer
    Pages 84-95
  11. Thomas Banchoff, John Wermer
    Pages 96-110
  12. Thomas Banchoff, John Wermer
    Pages 111-125
  13. Thomas Banchoff, John Wermer
    Pages 126-129
  14. Thomas Banchoff, John Wermer
    Pages 130-134
  15. Thomas Banchoff, John Wermer
    Pages 135-144
  16. Thomas Banchoff, John Wermer
    Pages 145-162
  17. Thomas Banchoff, John Wermer
    Pages 163-174
  18. Thomas Banchoff, John Wermer
    Pages 175-189
  19. Thomas Banchoff, John Wermer
    Pages 190-201
  20. Thomas Banchoff, John Wermer
    Pages 202-206
  21. Thomas Banchoff, John Wermer
    Pages 207-215
  22. Thomas Banchoff, John Wermer
    Pages 216-223
  23. Thomas Banchoff, John Wermer
    Pages 224-227
  24. Thomas Banchoff, John Wermer
    Pages 228-235
  25. Thomas Banchoff, John Wermer
    Pages 236-243
  26. Thomas Banchoff, John Wermer
    Pages 244-252
  27. Back Matter
    Pages 253-259

About this book

Introduction

In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a non-trivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of two-dimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.0-2.7. Then the very same outline is used in Chapters 3.0-3.7 to present the linear algebra of three-dimensional space, so that the former ideas are reinforced while new concepts are being introduced.

Keywords

Abstract algebra Eigenvalue Lineare Algebra algebra biology chemistry form geometry linear algebra quadratic form statistics transformation

Authors and affiliations

  • Thomas Banchoff
    • 1
  • John Wermer
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0161-5
  • Copyright Information Springer-Verlag New York 1983
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0163-9
  • Online ISBN 978-1-4684-0161-5
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site