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  • Textbook
  • © 1992

Linear Algebra Through Geometry

Authors:

  1. Thomas Banchoff

    1. Department of Mathematics, Brown University, Providence, USA

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    You can also search for this author in PubMed   Google Scholar

  2. John Wermer

    1. Department of Mathematics, Brown University, Providence, USA

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (35 chapters)

  1. Front Matter

    Pages i-xii
    PDF

  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
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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.
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Keywords

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Authors and Affiliations

  • Department of Mathematics, Brown University, Providence, USA

    Thomas Banchoff, John Wermer

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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: 978-0-387-97586-3Published: 25 November 1991

  • Softcover ISBN: 978-1-4612-8752-0Published: 19 March 2012

  • eBook ISBN: 978-1-4612-4390-8Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 2

  • Number of Pages: XII, 308

  • Topics: Linear and Multilinear Algebras, Matrix Theory, Geometry

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Access via your institution

Buy it now

eBook USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 74.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 74.95
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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