Linear Algebra

1. Front Matter

   Pages i-xii

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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

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.

• Eigenvalue
• Eigenvector
• Lineare Algebra
• Matrix
• Multilinear Algebra
• adopted textbook
• algebra
• linear algebra
• matrix theory

• Mathematisches Institut, Universität Göttingen, Gottingen, Germany

  Larry Smith

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