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-xii
  2. Thomas Banchoff, John Wermer
    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 39-49
  7. Thomas Banchoff, John Wermer
    Pages 50-60
  8. Thomas Banchoff, John Wermer
    Pages 61-74
  9. Thomas Banchoff, John Wermer
    Pages 75-84
  10. Thomas Banchoff, John Wermer
    Pages 85-97
  11. Thomas Banchoff, John Wermer
    Pages 98-112
  12. Thomas Banchoff, John Wermer
    Pages 113-116
  13. Thomas Banchoff, John Wermer
    Pages 117-121
  14. Thomas Banchoff, John Wermer
    Pages 122-132
  15. Thomas Banchoff, John Wermer
    Pages 133-150
  16. Thomas Banchoff, John Wermer
    Pages 151-162
  17. Thomas Banchoff, John Wermer
    Pages 163-177
  18. Thomas Banchoff, John Wermer
    Pages 178-189
  19. Thomas Banchoff, John Wermer
    Pages 190-196
  20. Thomas Banchoff, John Wermer
    Pages 197-204

About this book

Introduction

Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry.

Keywords

Eigenvalue Lineare Algebra Matrix algebra linear algebra

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4390-8
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8752-0
  • Online ISBN 978-1-4612-4390-8
  • Series Print ISSN 0172-6056
  • About this book