Handbook

Linear algebra is a key tool in all of mathematics and its applications. For example, the output of many electrical circuits depends linearly on the input (over moderate ranges of input), and successfully correcting the trajectory of a space probe involves repeatedly solving systems of linear equations in hundreds of variables. Linear methods are vital in ecological population models, and in mathematics itself. You have met systems of linear equations and matrices, vector spaces and linear transformations in first year Mathematics courses, without necessarily understanding all the subtleties involved. In MATH2501, you will review the material from first year, so that vector spaces and linear transformations become familiar friends rather than uneasy acquaintances. You will learn about geometric transformations: projections
(which can also be viewed as least squares approximations), rotations and reflections. You will see how to view many linear transformations as being made up of "stretches" in various directions, (the diagonalisation process), and the more general Jordan form. This will allow you to calculate functions of matrices (such as the exponential of a matrix) and hence to solve systems of linear differential equations.