Welcome to Week 1.
The Wednesday lecture this week will be given by Dr Kirsten Pfeiffer. Our work in linear algebra will start with matrices. Linear algebra is not just about matrices, but the study of matrices is a very big part of it. Also, matrices are very important practical and technical elements of the subject, and a good starting point that can lead to wider themes.
In Chapter 1 (Weeks 1 to 3 or so), the main point is that matrices are useful, and worthy of our attention. The first piece of evidence to support this assertion is the content of our lectures in Week 1 – the technique of Gaussian elimination (and Gauss-Jordan elimination), for solving systems of linear equations.
This method is classical and not at all new, but it continues to be the basis for many modern algorithms (see this article for a discussion of this point). It is an example where encoding data in matrix form gives a representation that is convenient for computation, and allows for a systematic approach to identifying all simultaneous solutions of a collection of linear equations.
Exceptionally this week, we will not have a lecture on Friday at our scheduled time. The video below is a substitute for Friday’s lecture. Please watch it before Wednesday of Week 2 if you can.
Also included below (for continuity and as a backup) is a video version of the preceding lecture. (Please ignore the lecture numbers referred to in the videos, they are not current).
Slides for lectures in Week 1.
Relevant sections of the lecture notes for this week are Sections 1.1 and 1.2.