Instructor: Dr. Iuliana Oprea
Department of Mathematics, Colorado State University
M10-10:50AM, W3-3:50PM and by appt.
The final exam: 9:10-11:10 am on Tuesday, 15 December, room E205
- General information
- Coursework and grades
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
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.
Linear Algebra, P. Lax, John Wiley & Sons,
Inc., 2-nd Edition, ISBN 0-471-75156-4
Matrix Analysis, R. Horn and C. Johnson, Cambridge University Press, ISBN
Linear Algebra in Action, Harry Dym, AMS Grad.
Studies in Math., Vol. 78, 2007. ISBN 0-8218-3813-X
Vector Spaces, P. Halmos, Springer, ISBN 3-540-90093-4
Operators, C. Lanczos, SIAM, 0-89871-370-6
Introduction to Matrix
Analysis, R. Bellman, McGraw-Hill, New
Methods of Mathematical
Physics, Vol. I, R. Courant
and D. Hilbert, Wiley Interscience, New York, 1953
Matrix Computations, G. Golub and C.
Van Loan, John Hopkins University Press, 1989
Linear Algebra, K. Hoffman and R. Kunze,
Prentice Hall, New Jersey,
Linear Algebra and its
Applications, G. Strang,
Harcourt, Brace, Jovanovich, San
(on-line free text book, undergrad
with solutions to all exercises): Jim Hefferon, Linear
- Lectures: MWF 2:00PM-2:50PM, Eng E205
Course work and grades
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%).