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

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