**M560** Fall
2007 Course:
**Linear Algebra**

__Instructor: Dr. Iuliana Oprea__

Department of Mathematics, Colorado State University

office:Weber
123, phone:1-6751,
office hours: M11-11:50AM,
W9-9:50AM and by appt.

*url:*
http://www.math.colostate.edu/~juliana

- Overview
- Prerequisites
- Textbook
- General information
- Coursework and grades
- Homework

**Overview**

The central
purpose
of this course is an investigation of the properties of linear
transformations on finite dimensional vector spaces. Along the way, we
will develop some properties of vector, Euclidean, and normed linear spaces. The
course material moves from the general and abstract to the particular.
We start by investigating general properties of linear transformations
on vector spaces,
we consider the consequences of the additional structures of inner
product and norms. Finally, we conclude by examining some particularly
important decompositions of linear
transformations. Along the way, we will consider a few interesting and
important applications.

**Prerequisites**

# It
would be wise to have taken a good course in linear algebra at the
undergraduate level, i.e., a course that went beyond simple matrix
manipulation. However, the desirable background could be obtained in
the context of other courses. Please speak to me if you have questions.

__Course Text__

Ø
*Linear Algebra, *P. Lax, John Wiley & Sons,
Inc., ISBN 0-471-11111-2

Ø
*Matrix Analysis, *R. Horn and C. Johnson, Cambridge University Press, ISBN
0-521-38632-2
__Supplemental Texts__

Ø
*Linear Algebra in Action, *Harry Dym, AMS Grad.
Studies in Math., Vol. 78, 2007. ISBN 0-8218-3813-X

Ø
*Finite Dimensional
Vector Spaces, *P. Halmos, Springer, ISBN 3-540-90093-4

Ø
*Linear Differential
Operators, *C. Lanczos, SIAM, 0-89871-370-6

Ø
*Introduction to Matrix
Analysis, *R. Bellman, McGraw-Hill, New
York, 1960

Ø
*Methods of Mathematical
Physics, Vol. I, *R. Courant
and D. Hilbert, Wiley Interscience, New York, 1953

Ø
*Matrix Computations, *G. Golub and C.
Van Loan, John Hopkins University Press, 1989

Ø
*Linear Algebra, *K. Hoffman and R. Kunze,
Prentice Hall, New Jersey,
1971

Ø
*Linear Algebra and its
Applications, *G. Strang,
Harcourt, Brace, Jovanovich, San
Diego, 1988

Ø
http://www.math.colostate.edu/~estep/education/560/main560.html

**General information**

- Lectures: MWF 10:00am-10:50am, Wagar 107B

- Office hours: M3-4PM, W8-9AM and by appt.

**Course work and grades**

# The
course work will consist of problem sets assigned periodically and a
cumulative two hour Final Exam. Grading will be based on
homeworks (70%) and the final exam (30%).

**Homework**

- HW1, due Wednesday, 5 September: Lax, Chapter 1, Exercises 3-6,
12-17
- HW2 due
September 14: Lax ex.1, p.11; ex. 2, p.12; ex 2,3, p. 19;
4,5 p. 20; problems 1, 2 from here,
- HW3 due
September 28: here,
- HW4 due
October 12: hard copy handed out in class, ask me if you need an extra
one