Linear Algebra 189-223A (sections 1 & 2)

Daniel Wise (coordinator)	Mak Trifkovic
Section 1. MWF 10:35-11:25.	Section 2. MWF 12:35-1:25.
923 Burnside, office hrs: Monday 8:45-9:45am, Wednesday 1:30-2:30pm.	1127 Burnside, office hrs: Monday 3-4pm, Wednesday 4-5pm
398-3850 wise@math.mcgill.ca	398-3803 mak@math.mcgill.ca

SPECIAL BONUS OFFICE HOURS

Saturday & Sunday 4-5pm

HW can be picked up at that time.

Text: D.C.Lay, Linear Algebra and its Applications (2^nd edition), Addison-Wesley, 1997.

This text is available at the bookstore. A “study guide” for Lay’s text is also available there.

Markers: Claude Gravel & Kelvin Lee

Midterm Exam: 2 hour exam covering material up to that point will be given on

Wednesday, October 30, 6-8pm in LEA 26. (priority #2). solutions

Final Exam: 3 hour exam covering the entire course, scheduled during official exam period. (2pm-5pm, Monday, December 16, 2002 [LEA 132])

Grades: Max( 20% HW + 25% Midterm + 55% Final, 100% Final)

Calculators: Neither required nor allowed.

Supplemental: There will be an official supplemental exam worth 100% of the mark.

Homework: There will be 13 assignments. They should be placed in the assignment box

on the 10^th floor of Burnside Hall by 4:55pm on the due date.

Late assignments will NOT be accepted. (The bottom two HW grades are dropped.)

Write your name, student number, and section number on your stapled assignments.

A random subset of the assigned problems will be marked by the Graders.

Mastery of the material (outlined below) requires that the students devote a significant amount of time to solving problems from the textbook.

Syllabus:

Chapters 1-3: Review:

Linear Equations in Linear Algebra (CH. 1: pp. 1-96)

Matrix Algebra (Ch 2; pp. 97-142, 165-178)

Determinants (Ch. 3; pp. 179-195)

Chapter 4: Vector Spaces (pp. 209-271, 282-293)

Vector spaces and subspaces.

Null-spaces, column-spaces, linear transformations.

Linearly independent sets, bases.

Coordinate systems.

The dimension of a vector space.

Rank. change of basis.

Applications to Markov chains.

Chapter 5. Eigenvalues and Eigenvectors (pp. 295-366)

Eigenvalues and eigenvectors.

The characteristic equation.

Diagonalization.

Eigenvectors and linear transformations.

Complex eigenvalues.

Discrete dynamical systems.

Applications to differential equations.

Chapter. 6. Orthogonality and least squares (pp. 367-440)

Inner product, length and orthogonality.

Orthogonal sets.

Orthogonal projections.

The Gram-Schmidt process.

Least-squares problems.

Applications to linear models.

Inner product spaces.

Applications of inner product spaces.

Chapter 7. Symmetric matrices and quadratic forms (pp. 441-476).

Diagonalization of symmetric matrices.

Quadratic forms.

Constrained optimization.

The singular value decomposition.