Syllabus for Math 4242 --- Spring 2006


One semester course on linear algebra. Assuming a basic acquaintance with vectors and matrices, the course goes on to study matrix theory in greater depth as well as some of its applications.Topics include Gauss elimination, LU factorization, row, column and null spaces and their dimensions, orthogonality, Gram-Schmidt method, QR factorization, determinants, eigenvalues, symmetric and Hermitian matrices and linear transformations. Applications include Markov chains, linear differential and difference equations, method of least squares, principle axes for conic sections, etc.


Applied Linear Algebra, by Olver and Shakiban. We will cover many, but not all, of the topics in the book. This is only possible because some of the material should already be familiar from previous courses. Specifically, you should already know about matrix multiplication, determinants of small matrices, and probably at least heard of eigenvalues.


There will be grades for quizzes, two midterm exams and a final exam. All exams and quizzes are open book/notes, calculators allowed. For a general university policy statement about grades, academic honesty and workload, go to: University Grading Policy Statement.

Quizzes 20 %
Midterm Exams (20 % each) 40 %
Final Exam 40 %

Exam Dates:

 Midterm I Wednesday, February 22
 Midterm II Wednesday, April 5
 Final Saturday, May 13, 1:30-3:30


Homework will be assigned but not collected. Instead there will be weekly quizzes consisting of problems very similar to the homework problems. If you can do the homework problems you should have no trouble with the quizzes. One quiz score will be dropped to allow for an absence or just a "bad day." To see the assignments, click on the link above.

Approximate Schedule:

 Week  Topic Reading
1/18-20 Gauss elimination, PA=LU 1.2-1.4
1/23-27 Inverses, LDL^T,Lin. systems 1.5-1.8
1/30-2/3 Determinants,vector spaces, span, lin.indep 1.9, 2.1-2.3
2/6-10 Basis,dimension, Fund.Th. 2.4-2.5
2/13-17 Inner products, norms 3.1-3.3
2/20-24 Midterm I
2/27-3/3 Pos. def. matrices, comp.square, complex vs 3.4-3.6
3/6-10 Minimization, least squares 4.1-4.4
3/13-17 Spring Break
3/20-24 Orthog. bases, Gram-Schmidt, orth.matrices 5.1-5.3
3/27-31 Orthog. poly., projection, subspaces 5.4-5.6
4/3-7 Midterm II
4/10-14 Linear transformations 7.1-7.3
4/17-21 Eigenvalues, diagonalization 8.1-8.3
4/24-28 Orthog. diagonlization, singular values 8.4-8.5
5/1-5 Linear differential equations, Markov chains 9.1-9.3, 10.4
5/13 Final Exam -- 1:30-3:30


Here are two do-it-yourself computer labs to see how Matlab can be used to numerically solve linear algebra problems. The links below allow you to download the instructions for the labs which can be done on any computer running Matlab. This is purely for enrichment -- no grades.

Lab 1
Lab 2