M560 Fall 2009 Course: Linear Algebra
Instructor: Dr. Iuliana Oprea
Department of Mathematics, Colorado State University
: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

  1. Overview
  2. Prerequisites
  3. Textbook
  4. General information
  5. Coursework and grades
  6. Homework


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.


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

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%).