Linear Algebra

Overview

This is a first course in linear algebra. The course will lay down the basic concepts and techniques of linear algebra needed for subsequent study. At the same time, it will provide an appreciation of the wide application of this discipline within the scientific field.

The course will require development of theoretical results. Proofs and consequences of such results will require the use of mathematical rigour, algebraic manipulation, geometry and numerics.

A goal of the course is to provide insight into how linear algebra theorems and results, sometimes quite abstract, impinge on everyday life. This will be illustrated with detailed examples.

Learning Outcomes

At the end of this course the student will be capable of gained the ability to:

• Comprehend vector spaces (subspaces).
• Understand fundamental properties of matrices including inverse matrices, eigenvalues and linear transformations.
• Be able to solve linear systems of equations.
• Have an insight into the applicability of linear algebra.