MAT-2-mi3/am3i
Linear Algebra Lecture Notes

JOSÉ FIGUEROA-O’FARRILL

Version of November 7, 2005.

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.

These notes contain a series of HowTo’s illustrating different computational techniques. These will be covered in lecture and are an integral part of the module. Many of the tutorial problems assume that you have mastered these techniques.

All tutorial problems, and not just those which are to be handed in, are an integral part of the module. Their results will be used freely in the lectures and will be assumed in other tutorial problems.

These notes do not contain everything which is covered in lectures. Some examples and proofs which appear in the lecture have not yet found their way into these notes.

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Indeed, these notes are still evolving, so I would be happy to receive comments, praise, criticisms, suggestions for improvement or corrections. I can be contacted by email at j.m.figueroa_at_ed.ac.uk.