Welcome to Week 1.

We have two main items of business this week, corresponding to our two lectures. The first is the introduction of the concept of a vector space (Lecture 1). Vector spaces are the main objects of attention in linear algebra, so this first lecture contains probably the most important definition in our course.

Here is Lecture 1

Slides for Lecture 1, annotated and without annotation.

The second theme is a review of matrix algebra. The algebra of matrices provides a computational and practical environment for the study of linear algebra. Almost every problem in linear algebra has a formulation in terms of matrices. And one of the nice things about matrices is that we can do calculations with them.

Here is Lecture 2

Slides for Lecture 2, annotated and without annotation.

The relevant sections of the lecture notes for this week are Section 1.1 (Vector Spaces) and Section 1.2 (Review of Matrix Algebra). Please remember that the lecture notes form the “official text” for the module, and they have more detail than the slides. You are expected to study them in addition to the lectures.