Quite an interesting chapter this one. It built up on the Isometries covered in Chapter A3 and moved over to describing them with matrices.
Was quite easy to work through as most of it was just combining materials covered previously. Though there were some new matrix techniques pushed into the mix as well |detAB|=|detA|*|detB| for example, which cut’s down a bit of work when working out scaling factors.
Combination of transformations was quite good as well, at least it’s now easier to look at a matrix and visualise what’s meant to be happening, before that it could be a bit trickier.
The section which bought in Affine Transformations was quite interesting as well.
The section on transformations of the unit circle was pretty confusing. The explanation of why you used A-1 rather than the just A wasn’t hugely well written. After some thinking about it and reading on the OU forums it’s a bit clearer, though I think it’s one of those things to just commit to memory rather than trying to work out why atm.
Has just left me wondering what happens when the transformations move from 2 dimension into 3 (or more). Wonder if that’s covered on later modules?