MATH203-12S2 (C) Semester Two 2012
Linear Algebra

Description

Linear algebra is a key part of the mathematical toolkit needed in the modern study of many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including orthogonality, projections and eigenvalues, with an emphasis on practical applications and use of the computer package MATLAB.

Topics covered:
Linear systems. Review of Gaussian elimination, partial pivoting. Partitioned matrices. LU factorizations, tridiagonal and band systems. Vector and matrix norms. Condition number. Error analysis. Iterative methods for solving systems of linear equations. Orthogonality, Gram-Schmidt process. QR factorization. Projections, projections as transformations. Least squares approximation. Orthogonal expansions, Fourier series. Eigenvalues and eigenvectors. Characteristic equation, diagonalization. Power method and variants. Hermitian and positive definite matrices, unitary matrices, normal matrices.

Applications:
Linear difference and differential equations, stability analysis; classification of quadratic varieties; recurrence relations; population models; Markov chains.

Learning Outcomes

At the end of the course, students will:

• be proficient in the standard techniques of matrix algebra and vector spaces: matrix factorizations (LU and QR); projections; diagonalization; iterative methods (Gauss-Seidel, power method) and convergence
• understand why these techniques work
• be able to use these techniques in a variety of applications, including using MATLAB to solve standard problems
• have developed problem solving skills both as part of a team and as an individual
• have developed written and oral communication skills, emphasizing the ability to explain what the mathematics means

Pre-requisites

Restrictions

For further information see Mathematics and Statistics.