M560 Fall 2006 Course: Linear Algebra
Instructor: Dr. Iuliana Oprea
Department of Mathematics, Colorado State University
office:Weber 123, phone:1-6751,
url: http://www.math.colostate.edu/~juliana

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

General information

Course work and grades

The course work will consist of problem sets assigned periodically and a cumulative two hour Final Exam.  Problems in the problem sets so marked by the instructor may be resubmitted.

Homework

HW1 due September   1: Lax 3-9 pag.3-4; Lax 15, Chapter 1; also show that X/Y linear space
HW2 due September 15: Lax 2,3 pag 19, 4,5 pag 20, Proof of Theorem 4, pag 23; problems 4, 5 from here, Show that P is projection then I-P is projection and Range(I-P) = Null(P)
HW3 due September 29 - ask instructor, if you missed the class
 HW4 due October 13 : hand out in class