# Linear Algebra

Textbook

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

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 40-53
8. Larry Smith
Pages 54-61
9. Larry Smith
Pages 62-86
10. Larry Smith
Pages 87-98
11. Larry Smith
Pages 99-106
12. Larry Smith
Pages 107-124
13. Larry Smith
Pages 125-145
14. Larry Smith
Pages 146-156
15. Larry Smith
Pages 157-182
16. Larry Smith
Pages 183-215
17. Larry Smith
Pages 216-245
18. Larry Smith
Pages 246-273
19. Back Matter
Pages 275-280

### 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

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 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
• 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
• Buy this book on publisher's site
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