Math 4500
Matrix Theory
Fall 2006
Instructor Bryan Shader
Office RH 321 (or RH 203)
Phone 766-6826
Email bshader@uwyo.edu
Office Hours M 10-11, W 11-12, Th 2:00-3:00 or by appointment
Grading
Homework 31%
2 Midterm Exams 23% each
1 Final Exam 23%
Homework
sets will be given about once a week. Your will be given one week
to complete each homework set. No late homework will be
accepted. Your homework solutions should be mathematically
correct and written in full mathematical sentences. The homework
will be a mix between computation, application of the theory taught in
class, real-world applications, and concepts. Feel free to ask me
specific questions (i.e. ones that show that you've already thought
about the problem and just need some help getting unstuck) about the
homework. It is okay to broadly discuss homework problems with other
students in the class. However, the main ideas of a solution and
the final work should be your own.
There is no required textbook for this course. Homework and exams will be base on the lectures.
A good reference book for the course is: Applied Linear Algebra by P. Olver and C. Shakiban
(Prentice Hall, 2006, ISBN 0-13-147382-4).
Matrix
theory is one of the fundamental areas of mathematics. It is used
in virtually every area of advanced mathematics, and over the past
century has been an important tool in various applications.
Accordingly, the goals of the course are two-fold:
- To develop a thorough conceptual understanding of, and proficient computational skills for matrix theory.
- To develop an understanding of how matrix theory is used in a variety of applications.
Topics
to be covered include: linear transformations, spectra of matrices,
similarity, Jordan Canonical Form, inner products, unitary and normal
matrices, the Singular Value Decomposition, and the Perron-Frobenius
theory of nonnegative matrices. Some applications that we
will (hopefully) encounter are: the Discrete Fourier Transform, the
Fast Fourier Transform, basic signal processing, population modeling,
data compression, face recognition, least squares and date base
searches.
A positive attitude toward learning and a willingness to work are required. Ask question, come to
office hours, carefully go over your notes (several times), and enjoy learning something new!
Solutions to Final Review and Optional Homework
Solutions to Review for Exam 2
Solutions to Review for Exam 1 (Part 1)
Solutions to Review for Exam 1 (Part 2)
Lectures 10-15
Lectures 20-30
Lecture 13
Lecture 14
Lecture 15
Lecture 16
Lecture 17
Lecture 18
Lecture 19
Lecture 20
Lecture 21
Lecture 22
Lecture 23
Lecture 24
Lecture 25
Lecture 26
Lecture 27
Lecture 28
Lecture 29
Lecture 30
Lecture 31
Lecture 32
Lecture 33
Lecture 34
Lecture 35
Lecture 36
Lecture 37
Lecture 38
Lecture 39
Lecture 40
Lecture 41
Lecture 42