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Linear Algebra

  • Textbook
  • © 1978

Overview

Authors:
  1. Larry Smith

    1. Mathematisches Institut, Universität Göttingen, Göttingen, West Germany
      Department of Mathematics, Indiana University, Bloomington, USA

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-vii
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  2. Vectors in the plane and space

    • Larry Smith
    Pages 1-12

  3. Vector spaces

    • Larry Smith
    Pages 13-19

  4. Subspaces

    • Larry Smith
    Pages 20-25

  5. Examples of vector spaces

    • Larry Smith
    Pages 26-32

  6. Linear independence and dependence

    • Larry Smith
    Pages 33-39

  7. Bases and finite-dimensional vector spaces

    • Larry Smith
    Pages 40-53

  8. The elements of vector spaces: a summing up

    • Larry Smith
    Pages 54-61

  9. Linear transformations

    • Larry Smith
    Pages 62-86

  10. Linear transformations: some numerical examples

    • Larry Smith
    Pages 87-98

  11. Matrices and linear transformations

    • Larry Smith
    Pages 99-106

  12. Matrices

    • Larry Smith
    Pages 107-124

  13. Representing linear transformations by matrices

    • Larry Smith
    Pages 125-145

  14. More on representing linear transformations by matrices

    • Larry Smith
    Pages 146-156

  15. Systems of linear equations

    • Larry Smith
    Pages 157-182

  16. The elements of eigenvalue and eigenvector theory

    • Larry Smith
    Pages 183-215

  17. Inner product spaces

    • Larry Smith
    Pages 216-245

  18. The spectral theorem and quadratic forms

    • Larry Smith
    Pages 246-273

  19. Back Matter

    Pages 275-280
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Keywords

About this book

This text is written for a course in linear algebra at the (U.S.) sophomore undergraduate level, preferably directly following a one-variable calculus course, so that linear algebra can be used in a course on multidimensional calculus. Realizing that students at this level have had little contact with complex numbers or abstract mathematics the book deals almost exclusively with real finite-dimensional vector spaces in a setting and formulation that permits easy generalization to abstract vector spaces. The parallel complex theory is developed in the exercises. The book has as a goal the principal axis theorem for real symmetric transformations, and a more or less direct path is followed. As a consequence there are many subjects that are not developed, and this is intentional. However a wide selection of examples of vector spaces and linear trans­ formations is developed, in the hope that they will serve as a testing ground for the theory. The book is meant as an introduction to linear algebra and the theory developed contains the essentials for this goal. Students with a need to learn more linear algebra can do so in a course in abstract algebra, which is the appropriate setting. Through this book they will be taken on an excursion to the algebraic/analytic zoo, and introduced to some of the animals for the first time. Further excursions can teach them more about the curious habits of some of these remarkable creatures.

Authors and Affiliations

  • Mathematisches Institut, Universität Göttingen, Göttingen, West Germany

    Larry Smith

  • Department of Mathematics, Indiana University, Bloomington, USA

    Larry Smith

Bibliographic Information

  • Book Title: Linear Algebra

  • Authors: Larry Smith

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4615-9995-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag, New York Inc. 1978

  • Softcover ISBN: 978-1-4615-9997-5Published: 23 January 2012

  • eBook ISBN: 978-1-4615-9995-1Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: VII, 280

  • Topics: Linear and Multilinear Algebras, Matrix Theory

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