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- About this Textbook
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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.
- Table of contents (17 chapters)
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Vectors in the plane and space
Pages 1-12
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Vector spaces
Pages 13-19
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Subspaces
Pages 20-25
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Examples of vector spaces
Pages 26-32
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Linear independence and dependence
Pages 33-39
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Table of contents (17 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Linear Algebra
- Authors
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- L. Smith
- Series Title
- Undergraduate Texts in Mathematics
- Copyright
- 1978
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer-Verlag, New York Inc.
- eBook ISBN
- 978-1-4615-9995-1
- DOI
- 10.1007/978-1-4615-9995-1
- Series ISSN
- 0172-6056
- Edition Number
- 1
- Number of Pages
- VII, 280
- Topics
