**M560** Fall
2009 Course:
**Linear Algebra**

__Instructor: Dr. Iuliana Oprea__

Department of Mathematics, Colorado State University

office:Weber
123, phone:1-6751,
office hours:
M10-10:50AM, W3-3:50PM and by appt.

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

The final exam: 9:10-11:10 am on Tuesday, 15 December, room E205

- 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., 2-nd Edition, ISBN 0-471-75156-4

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

(on-line free text book, undergrad
level,
with solutions to all exercises): *Jim Hefferon, Linear
Algebra*: http://joshua.smcvt.edu/linalg.html

**General information**

- Lectures: MWF 2:00PM-2:50PM, Eng E205

**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%).