ARCHIVE PAGE

This page is not updated any more.

ABSTRACT LINEAR ALGEBRA
(MATH 4164-001, Spring 2008)

Instructor: Gábor Hetyei
Office: Fretwell 335F, Phone: 867-2543, E-mail: ghetyei@uncc.edu
Tuesday 3:05-4:35 pm, Thursday 2:25-3:25 pm, or by appointment.
Text: Linear Algebra, 4th Edition by Stephen H. Friedberg, Arnold J. Insel and Lawrence E. Spence. ISBN: 0-13-008451-4.
Some information may be provided on supplementary handouts, and you can not expect everything told in the lecture to be found in the book. Attendance is mandatory!
Prerequisite: MATH 3163 and MATH 2164, or consent of the department.
Topics: Chapter 1: vector spaces, subspaces, linear combinations, linear dependence, bases, maximal linearly independent subsets
Chapter 2: linear transformations, null spaces and ranges, matrix representations, composition and matrix multiplication, invertibility, change of coordinates, dual spaces
Chapter 3: elementary matrix operations, rank, systems of linear equations
Chapter 4: determinants of order n, properties and facts
Chapter 5: eigenvalues, eigenvectors, diagonalization, invariant subspaces and the Cayley-Hamilton theorem
Chapter 6: inner products, Gram-Schmidt orthogonalization
Chapter 7: Jordan canonical form

Time permitting, and depending on the interest of the audience, we will also cover some of the following: characterization of the determinant as an alternating multilinear function, adjoint operators, unitary and orthogonal operators, bilinear and quadratic forms, the geometry of orthogonal operators, minimal polynomial.
Test Dates:
Test 1 Tuesday, February 12, 2008.
Test 2 Tuesday, March 25, 2007.
Final Exam Tuesday May 6, 5:00 - 7:45 p.m.
(Double-check in the UNCC Exam schedule !)
The final exam will be cumulative, consisting of two parts. The first part will be mandatory, covering only material taught after Test 2. The second half will contain questions reviewing the material taught before Test 2. This part will be optional, if left unanswered, I will substitute the average of your test scores.
Homework: Homework will be assigned every week, and will be usually collected on next Tuesday. I will make an effort to regularly post the homework on the webpage
http://www.math.uncc.edu/~ghetyei/courses/4164/hw.html
In case of discrepancy, what I said in class is "official". A random selection of the assigned exercises will be graded. Past due assignments will be counted at the rate of 90% of their value. No credit will be given for solutions submitted after we discussed them in class.
Evaluation: Grades will be based on: 23% for the homework, 22% for each of the tests, and 33% for the final (22% for the mandatory part, 11% for the optional part).
Class meeting: Tuesdays 5:00 - 7:45 pm in Denny 109.
Homepage: http://www.math.uncc.edu/~ghetyei/courses/4164/index.html