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.