Linear Algebra

1. Front Matter

   Pages I-IX

   PDF

2. Sets and Maps

   • Klaus Jänich

   Pages 1-14

3. Vector Spaces

   • Klaus Jänich

   Pages 15-42

4. Dimension

   • Klaus Jänich

   Pages 43-61

5. Linear Maps

   • Klaus Jänich

   Pages 62-84

6. Matrix Calculus

   • Klaus Jänich

   Pages 85-102

7. Determinants

   • Klaus Jänich

   Pages 103-119

8. Systems of Linear Equations

   • Klaus Jänich

   Pages 120-135

9. Euclidean Vector Spaces

   • Klaus Jänich

   Pages 136-150

10. Eigenvalues

    • Klaus Jänich

    Pages 151-161

11. The Principal Axes Transformation

    • Klaus Jänich

    Pages 162-170

12. Classification of Matrices

    • Klaus Jänich

    Pages 171-186

13. Answers to the Tests

    • Klaus Jänich

    Pages 187-199

14. Back Matter

    Pages 200-205

    PDF

The original version of this book, handed out to my students in weekly in­ stallments, had a certain rugged charm. Now that it is dressed up as a Springer UTM volume, I feel very much like Alfred Dolittle at Eliza's wedding. I hope the reader will still sense the presence of a young lecturer, enthusiastically urging his audience to enjoy linear algebra. The book is structured in various ways. For example, you will find a test in each chapter; you may consider the material up to the test as basic and the material following the test as supplemental. In principle, it should be possible to go from the test directly to the basic material of the next chapter. Since I had a mixed audience of mathematics and physics students, I tried to give each group some special attention, which in the book results in certain sections being marked· "for physicists" or "for mathematicians. " Another structural feature of the text is its division into laconic main text, put in boxes, and more talkative unboxed side text. If you follow just the main text, jumping from box to box, you will find that it makes coherent reading, a real "book within the book," presenting all that I want to teach.

• Eigenvalue
• Eigenvector
• Matrix
• Rank–nullity theorem
• algebra
• linear algebra

• NWF I—Mathematik, Universität Regensburg, Regensburg, Germany

  Klaus Jänich

Policies and ethics