© 1978

Linear Algebra


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

Table of contents

  1. Front Matter
    Pages i-vii
  2. Larry Smith
    Pages 1-12
  3. Larry Smith
    Pages 13-19
  4. Larry Smith
    Pages 20-25
  5. Larry Smith
    Pages 26-32
  6. Larry Smith
    Pages 33-39
  7. Larry Smith
    Pages 62-86
  8. Larry Smith
    Pages 99-106
  9. Larry Smith
    Pages 107-124
  10. Larry Smith
    Pages 157-182
  11. Larry Smith
    Pages 216-245
  12. Larry Smith
    Pages 246-273
  13. Back Matter
    Pages 275-280

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.


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Authors and affiliations

  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenWest Germany
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

Bibliographic information

  • Book Title Linear Algebra
  • Authors L. Smith
  • Series Title Undergraduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90235-7
  • Softcover ISBN 978-1-4615-9997-5
  • eBook ISBN 978-1-4615-9995-1
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages VII, 280
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Linear and Multilinear Algebras, Matrix Theory
  • Buy this book on publisher's site
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