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Lecture notes
The course is based on lecture notes and not on any textbook. This year's course will be based on the lecture notes from last year, and they will be updated throughout the semester.
- Last update: 18.11 (Fixed typos)
- Updated chapters: All.
If you find typos or other mistakes in the notes, please contact Eirik.
Changes
Mistakes and typos in the lecture notes will be corrected throughout the semester. For the benefit of those who prefer to print the notes, we keep a list of the changes we make below. You should correct these mistakes in your printed copy of the notes.
| Page | Change | When |
|---|---|---|
| 108 | In part ii) of Thm 7.25, should be y in Cn, not y in Cm | 18.11 |
| 95-97 | In chapter 7.2, we are always working with square matrices: n=m. So change mxn to nxn. | 15.11 |
| 102 | In Corollary 7.18, A*A is an nxn-matrix and AA* is an mxm-matrix. Originally the opposite was stated. | 15.11 |
| 102 | Error in the last part of the proof of Proposition 7.17. | 13.11 |
| 108 | In Theorem 7.25i), the last sentence should read norm(y) > norm(z) (not norm(y) < norm(z)) | 12.11 |
| 82 | In eq 6.2, norm(x)+norm(y)→ norm(x)-norm(y) | 12.11 |
| 95 | In prop. 7.9, we need m=n. | 12.11 |
| 22 | In Lem 2.11, added that q is the conjugate of p. | 28.10 |
| 68 | In first line of proof of Thm 5.4, x in M → x in X. | |
| 44 | In the completion theorem, we added that the embedding is isometric. | 21.10 |
| 43 | In theorem 3.14, norm(f-t) → norm(f-t)<ε | 15.10 |
| 66 | Typo on line 9 from the bottom norm(z-y) → norm(z-x) | 14.10 |
| 4 | Typo: in definition of X\Y, the symbol should say "z is not in Y", but said z≠Y. | 09.10 |
| 37 | Typo: In the text before exercise 3.2.1, "complex numbers" → "rational numbers". | 04.10 |
| 33 | Typo in definition 3.1.4: the the definition of diam(A) needs x,y in A, not x,y in X. | 28.09 |
| 44 | Typo in the definition of L_p norm (upper limit p→b) | 25.09 |
| 23 | In the case of equality for Cauchy-Schwartz' inequality, we have added the assumption that both vectors are nonzero. | 07.09 |
| 14 | Typo in part (3) of lemma 2.1. | 09.09 |
Books
Based on the diverse student body taking this course it is a difficult task to recommend books for the material. Below are some suggestions but I encourage you to visit the library and browse through the available literature and look if there are sources on the web that you find helpful.
| Book | Relevant chapters | Description |
|---|---|---|
| Lax: Linear Algebra and its Applications, 2nd ed., Wiley. | 1-8, 14-15. Appendices: A,B. | The text develops the material from the perspective of functional analysis and applications in various areas. |
| Friedberg et. al.: Linear Algebra, 4th ed, Pearson.1) | 1.1–1.6, 2.1–2.6, 3.1 (repetition), 3.2, 3.4, Chapter 4 (repetition), 5.1, 5.2, 5.4, 6.1–6.8, 7.1–7.2. Appendices: A,B. | The book gives a thorough introduction to linear algebra. |
| Strang: Linear algebra and its applications. | 1.2–1.6, 2.1–2.4, 2.6, 3.1, 3.3–3.4, Chapter 4 (repetition), 5.1–5.2, 5.5–5.6, 6.1–6.3. Appendix B. | This book contains a wealth of examples on many aspects of linear algebra. |
| Kreyszig: Introductory Functional Analysis with Applications, John Wiley & Sons. Selected material from this book will be available at the department office for a small fee. | Chapter 1, 2.1–2.4, 2.6–2.10, 3.1–3.5, 3.8–3.10, Chapter 5, 7.1. Appendices: A.1.1–A.1.2, A.1.6.2) | The book by Kreyszig provides basic facts about functional analysis for anyone with a knowledge of linear algebra and calculus. |
| Young: An introduction to Hilbert space, Cambridge University Press. | Chapters 1–4 and 6–7. | An elegant introduction to Hilbert spaces. |