Compute exp of the 2-by-2 matrix 0, x, 0, 0 and exp of the 3-by-3 matrix 0, a, c, 0, 0, b, 0, 0, 0.

# Week 1

## Session 1

This is the first session, which will just be an introduction to the course. No pre-class material. Details are summarised here:

## Session 2

### Pre-class videos

Most sessions will only have 20-40 minutes of pre-class videos. This "feature-length" session 1 is there:

to get us quickly to the point where we can answer questions and get started on in-depth projects;

to give us more time to focus on the deeper ideas later in the course.

### Pre-class exercises

Exercise:

Exercise:

Verify the Baker-Campbell-Hausdorff formula for exp of the 3-by-3 matrix 0, a_1, c_1; 0, 0, b_1; 0, 0, 0 times exp of the 3-by-3 matrix 0, a_2, c_2; 0, 0, b_2; 0, 0, 0. [Hint: In this case, the formula is \exp\left(X+Y+\frac{1}{2}[X,Y]\right) with no further correction terms. Can you see why?]

## Optional extras