TEXT

Peter Lax, Linear Algebra, Wiley-Interscience

TOPICS

• A quick review of basic principles of linear independence, spanning sets, bases, and dimension.
• Quotient and dual spaces
• A quick review of the algebra of linear transformations, matrix representations of linear transformations, and determinants.
• Spectral Theory of Square Matrices leading to the Jordan Canonical Form
• Euclidean Structure; the Spectral Theory of Self-Adjoint Matrices
• Calculus of Vector and Matrix Valued Functions
• Normed Linear Spaces
• Perron-Frobenius results on positive matrices. Applications to asymptotics of Markov chains.
• Iterative schemes for solving systems of linear equations.

ASSIGNMENTS

Weekly problem sets due on Thursdays (usually) before lectures at 1:15 pm. Work on these assignments will account for 35% of your grade. Except in cases of illness or other extenuating circumstances, no late homework papers will be accepted after the time on the day due. Assignments may be found bellow.

• Homework 1
• Homework 2
• Homework 3
• Homework 4
• Homework 5
• Homework 6
• Homework 7
• Homework 8
• Homework 9
• Homework 10
• Homework 11

PROBLEM SESSIONS

Weekly problem sessions will be on Tuesdays from 5:00--6:00 p.m. at BK134. Please feel free to come to the problem sessions if you have any questions.

HOMEWORK KEYS

We will hand out homework keys for all assignments for the purpose of reviewing for exams.

EXAMS

Midterm Exam will account for 30% of the course grade. Probable dates: Thursday, March 10. Take-home final will account for 35% of the course grade.

COMPUTER SOFTWARE

Rather than do tedious hand calculations, we will rely on mathematical applications software (Maple, MatLab, etc.) in some of our work. You may use your favorite mathematical package, but I will take Maple as the class standard. Training in using Maple will be provided.

OFFICE HOURS

Tuesdays 2:30--3:30 p.m., Fridays 10:00--11:00 a.m., Olin 1279. Also available by appointment and most any time I am in my office in Olin 1279.
Office phone: Ext.18929;

E-mail: gu@math.hmc.edu.