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Linear Algebra

  • Textbook
  • © 1998

Overview

Authors:
  1. Larry Smith

    1. Mathematisches Institut, Universität Göttingen, Gottingen, Germany

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

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Vectors in the Plane and in Space

    • Larry Smith
    Pages 1-14

  3. Vector Spaces

    • Larry Smith
    Pages 15-23

  4. Examples of Vector Spaces

    • Larry Smith
    Pages 25-33

  5. Subspaces

    • Larry Smith
    Pages 35-45

  6. Linear Independence and Dependence

    • Larry Smith
    Pages 47-56

  7. Finite-Dimensional Vector Spaces and Bases

    • Larry Smith
    Pages 57-74

  8. The Elements of Vector Spaces: A Summing Up

    • Larry Smith
    Pages 75-83

  9. Linear Transformations

    • Larry Smith
    Pages 85-112

  10. Linear Transformations: Examples and Applications

    • Larry Smith
    Pages 113-128

  11. Linear Transformations and Matrices

    • Larry Smith
    Pages 129-157

  12. Representing Linear Transformations by Matrices

    • Larry Smith
    Pages 159-183

  13. More on Representing Linear Transformations by Matrices

    • Larry Smith
    Pages 185-198

  14. Systems of Linear Equations

    • Larry Smith
    Pages 199-226

  15. The Elements of Eigenvalue and Eigenvector Theory

    • Larry Smith
    Pages 227-265

  16. Inner Product Spaces

    • Larry Smith
    Pages 267-306

  17. The Spectral Theorem and Quadratic Forms

    • Larry Smith
    Pages 307-341

  18. Jordan Canonical Form

    • Larry Smith
    Pages 343-380

  19. Application to Differential Equations

    • Larry Smith
    Pages 381-404

  20. The Similarity Problem

    • Larry Smith
    Pages 405-410
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Keywords

About this book

This popular and successful text was originally written for a one-semester course in linear algebra at the sophomore undergraduate level. Consequently, the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permits easy generalization to abstract vector spaces. A wide selection of examples of vector spaces and linear transformation is presented to serve as a testing ground for the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, after the principal axis theorem. To achieve these goals in one semester it is necessary to follow a straight path, but this is compensated by a wide selection of examples and exercises. In addition, the author includes an introduction to invariant theory to show that linear algebra alone is incapable of solving these canonical forms problems. This bookis a compact but mathematically clean introduction to linear algebra with particular emphasis on topics in abstract algebra, the theory of differential equations, and group representation theory.

Authors and Affiliations

  • Mathematisches Institut, Universität Göttingen, Gottingen, Germany

    Larry Smith

Bibliographic Information

  • Book Title: Linear Algebra

  • Authors: Larry Smith

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1670-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-387-98455-1Published: 28 May 1998

  • Softcover ISBN: 978-1-4612-7238-0Published: 17 October 2012

  • eBook ISBN: 978-1-4612-1670-4Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 3

  • Number of Pages: XII, 454

  • Topics: Linear and Multilinear Algebras, Matrix Theory

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