Advertisement

Linear Algebra

  • Larry Smith

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

Introduction

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.

Keywords

Eigenvalue Eigenvector Lineare Algebra Vector space adopted textbook algebra calculus complex number linear algebra matrices quadratic form testing time transformation variable

Authors and affiliations

  • Larry Smith
    • 1
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenWest Germany
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-9995-1
  • Copyright Information Springer-Verlag New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4615-9997-5
  • Online ISBN 978-1-4615-9995-1
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site
Industry Sectors
Pharma
Automotive
Finance, Business & Banking
Electronics
Telecommunications
Aerospace
Oil, Gas & Geosciences