These are the lecture notes and tutorial problems for the Linear Algebra module in Mathematics for Informatics 3 (MAT-2-mi3/am3i). They are a revised version of the ones used in the 2004-2005 session, which were themselves revised due to changes in the syllabus from the ones used in the 2003-2004 session. The original lecture notes have benefited from extant notes on linear algebra by John Meldrum and on polynomials by Andrew Ranicki.
Linear algebra is the study of vector spaces and linear maps. The module is divided into three parts. During the first part, which will take up about half of the semester, we will study real vector spaces and their linear maps. We will discuss subspaces, linear (in)dependence, bases, dimension, linear maps and linear transformations and their relation to matrices, the effect of changing basis, eigenvalues and eigenvectors and diagonalisation. The second part will be devoted to univariate polynomials. The third and final part will serve as an introduction to algebraic coding theory, concentrating for definiteness on binary linear codes.