Linear Algebra 1

Module code: MA1115

Linear Algebra is an essential prerequisite for nearly all other areas of mathematics, from pure mathematical areas including algebra, geometry and analysis, via probability and statistics, and applied mathematics such as solving differential equations and numerical analysis, to physical topics such as quantum mechanics. Methods of Linear Algebra are used also in, for example, CT scans, cryptography, genetics, models for human hearing, computer graphics and certain economic models. And of course, Google’s success comes largely from its algorithm which ranks the importance of webpages according to an eigenvector of a weighted link matrix: for this to work, one needs to understand how to solve large systems of billions of equations with billions of unknowns efficiently!

In this module, along with its sequel MA1116, we will introduce and work on the fundamental concepts of Linear Algebra. This course will focus on linear systems and linear transformations, including the ubiquitous notion of eigenvalues and eigenvectors. A key focus will be to interpret transformations and solutions of systems geometrically. A fundamental tool in all of this is the concept of matrix operations, and so along the way we will study several important properties of matrices, and algorithms for inverting or transforming them in order to solve linear systems.