Franz Lemmermeyer

# Linear Algebra

### Schedule

```  TU  9:40 - 10:30, EB 103
TH 10:40 - 12:30, EB 103 ```
My grader this semester is Pinar Pekcagliyan.
The book we will use is Kolman and Hill, Elementary Linear Algebra. There will be two midterms, a final, quizzes, and homework.

### Topics

• Vector spaces.
• Linear independence, bases
• Coordinates
• Inner products
• Linear Maps
• Eigenvalues, eigenvectors
• Determinants
• Orthogonal Bases

### Homework

Homework is always due one week after hand-out except when stated otherwise. Solutions will be posted after all students have turned their homework in.

### Extra Problems

Here are some extra problems For practicing simple proofs.

### Schedule

I will not be able (nor do I want to) tell you everything in class that is in the book. It would help (you) if you came to class prepared: this means reading the part of the book I intend to cover. Since I only have the 7th edition, the numbering of the chapters may differ (in the 8th edition, Chapter 1 is split into two chapters, and Chapter 2 has therefore become Chapter 3).
• Tu 13.09.05: vectors, vector spaces (2.1-2.2)
• Th 15.09.05: subspaces, span 2.3 (2.4)
• Tu 20.09.05: 2.4
• Th 22.09,05: isomorphisms
• Tu 27.09.05: isomorphisms
• Th 29.09.05: test (solutions), matrices
• Tu 04.10.05: linear systems
• Th 06.10.05: rank of matrices, null space
• Tu 11.10.05: examples; applications
• Th 13.10.05: the dot product (not part of midterm 1)
• Tu 18.10.05: review
• Th 20.10.05: Midterm I, 10:40, usual class room. Here are lists of problems from the book (7th and 8th ed.) you should be able to do. Here is last years midterm 1 and the solutions to problems 2 and 4.
Here are the midterm and the solutions.
• Tu 25.10.05: discussion of midterm 1; inner product spaces.
• Th 27.10.05: inner product spaces; Gram-Schmidt
• Tu 01.11.05: orthogonal complements
• Th 03.11.05: NO CLASS
• Tu 08.11.05: direct sums; Fourier analysis
• Th 10.11.05: Kernel and image (range) of a linear map
• Tu 15.11.05: projections; complex vector spaces
• Th 17.11.05: Determinants
• Tu 22.11.05: Determinants
• Th 24.11.05: Eigenvalues
• Mo 28.11.05, 5:40 Problem Session
• Tu 29.11.05: Eigenvalues
• Th 01.12.05: Midterm 2 (inner product spaces, linear maps, determinants). Here is last year's exam (now including hints). For the solutions, see Degtyarev's page. Here are the midterm and the solutions.
• Tu 06.12.05: Discussion of midterm 2
• Th 08.12.05: No Class Moved to Mo, 28.11.05, 17:40
• Tu 13.12.05: Eigenvectors
• Th 15.12.05: Diagonalization
• Mo 19.12.05, 10:40 - 12:30; Last Class. Here are a few Problems
• Su 25.12.05, 15:30 - 17:30 FINAL in SAZ-04, SAZ-18 (CHANGE OF SCHEDULE!) Here are the solutions. The average was 52; if I disregard the three exams with only the names on them, it is 57.