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  • Textbook
  • © 1992

Linear Algebra Through Geometry

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

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  • ISBN: 978-1-4612-4390-8
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Table of contents (35 chapters)

  1. Front Matter

    Pages i-xii
  2. Vectors in the Line

    • Thomas Banchoff, John Wermer
    Pages 1-2
  3. The Geometry of Vectors in the Plane

    • Thomas Banchoff, John Wermer
    Pages 3-22
  4. Transformations of the Plane

    • Thomas Banchoff, John Wermer
    Pages 23-28
  5. Linear Transformations and Matrices

    • Thomas Banchoff, John Wermer
    Pages 29-38
  6. Products of Linear Transformations

    • Thomas Banchoff, John Wermer
    Pages 39-49
  7. Inverses and Systems of Equations

    • Thomas Banchoff, John Wermer
    Pages 50-60
  8. Determinants

    • Thomas Banchoff, John Wermer
    Pages 61-74
  9. Eigenvalues

    • Thomas Banchoff, John Wermer
    Pages 75-84
  10. Classification of Conic Sections

    • Thomas Banchoff, John Wermer
    Pages 85-97
  11. Vector Geometry in 3-Space

    • Thomas Banchoff, John Wermer
    Pages 98-112
  12. Transformations of 3-Space

    • Thomas Banchoff, John Wermer
    Pages 113-116
  13. Linear Transformations and Matrices

    • Thomas Banchoff, John Wermer
    Pages 117-121
  14. Sums and Products of Linear Transformations

    • Thomas Banchoff, John Wermer
    Pages 122-132
  15. Inverses and Systems of Equations

    • Thomas Banchoff, John Wermer
    Pages 133-150
  16. Determinants

    • Thomas Banchoff, John Wermer
    Pages 151-162
  17. Eigenvalues

    • Thomas Banchoff, John Wermer
    Pages 163-177
  18. Symmetric Matrices

    • Thomas Banchoff, John Wermer
    Pages 178-189
  19. Classification of Quadric Surfaces

    • Thomas Banchoff, John Wermer
    Pages 190-196
  20. Vector Geometry in n-Space, n ≥ 4

    • Thomas Banchoff, John Wermer
    Pages 197-204

About this book

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
  • matrix theory

Authors and Affiliations

  • Department of Mathematics, Brown University, Providence, USA

    Thomas Banchoff, John Wermer

Bibliographic Information

  • Book Title: Linear Algebra Through Geometry

  • Authors: Thomas Banchoff, John Wermer

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-4390-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1992

  • Hardcover ISBN: 978-0-387-97586-3

  • Softcover ISBN: 978-1-4612-8752-0

  • eBook ISBN: 978-1-4612-4390-8

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 2

  • Number of Pages: XII, 308

  • Topics: Linear Algebra, Geometry

Buying options

eBook
USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-4390-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 74.95
Price excludes VAT (USA)
Hardcover Book
USD 74.95
Price excludes VAT (USA)