Foundations of Linear Algebra

1. Front Matter

   Pages i-viii

   PDF

2. Basic Notation and Terminology

   • Jonathan S. Golan

   Pages 1-2

3. Fields and Integral Domains

   • Jonathan S. Golan

   Pages 3-11

4. Vector Spaces

   • Jonathan S. Golan

   Pages 12-23

5. Linear Independence and Dimension

   • Jonathan S. Golan

   Pages 24-40

6. Linear Transformations

   • Jonathan S. Golan

   Pages 41-54

7. Endomorphism Rings of Vector Spaces

   • Jonathan S. Golan

   Pages 55-64

8. Representation of Linear Transformations by Matrices

   • Jonathan S. Golan

   Pages 65-75

9. Rings of Square Matrices

   • Jonathan S. Golan

   Pages 76-92

10. Systems of Linear Equations

    • Jonathan S. Golan

    Pages 93-110

11. Determinants

    • Jonathan S. Golan

    Pages 111-126

12. Eigenvectors and Eigenvalues

    • Jonathan S. Golan

    Pages 127-143

13. The Jordan Canonical Form

    • Jonathan S. Golan

    Pages 144-153

14. The Dual Space

    • Jonathan S. Golan

    Pages 154-160

15. Inner Product Spaces

    • Jonathan S. Golan

    Pages 161-182

16. Endomorphisms of Inner Product Spaces

    • Jonathan S. Golan

    Pages 183-197

17. The Moore-Penrose Pseudoinverse

    • Jonathan S. Golan

    Pages 198-203

18. Bilinear Transformations and Forms

    • Jonathan S. Golan

    Pages 204-218

19. Algebras Over A Field

    • Jonathan S. Golan

    Pages 219-227

20. Back Matter

    Pages 228-237

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This book is an extensively revised version of my textbook "¥esodot HaAlgebra HaLiniarit" (The Foundations of Linear Algebra) used at many universities in Israel. It is designed for a comprehensive one-year course in linear algebra (112 lecture hours) for mathematics majors. Therefore, I assume that the student already has a certain amount of mathematical background - including set theory, mathematical induction, basic analytic geometry, and elementary calculus - as wellas a modicum of mathematical sophistication. My intention is to provide not only a solid basis in the abstract theory of linear algebra, but also to provide examples of the application of this theory to other branches ofmathematics and computer science. Thus, for example, the introduction of finite fields is dictated by the needs of students studying algebraic coding theory as an immediate followup to their linear algebra studies. Many of the students studying linear algebra either are familiar with the care and feeding of computers before they begin their studies or are simultaneously en­ rolled in an introductory computer science course. Therefore, consideration of the more computational aspects of linear algebra - such as the solution of systems of linear equations and the calculation of eigenvalues - is delayed until all students are assumed able to write computer programs for this purpose. Beginning with Chap­ ter VII, there is an implicit assumption that the student has access to a personal computer and knows how to use it.

• Eigenvalue
• Eigenvector
• Matrix
• algebra
• linear algebra
• matrix theory

• Department of Mathematics and Computer Science, University of Haifa, Haifa, Israel

  Jonathan S. Golan

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