Category Archives: Linear Algebra

Linear Algebra Feedback

Received another good mark for this assignment, which I'm happy about as at the last minute I realised I'd messed one question up so re-did it. Though despite the high mark, I had a lot of great feedback from my tutor.

Overwhelmingly, he mentioned that I had to use more English to explain why I was solving a question in a certain way. This struck a chord with me as the more solutions I read, the less English there appears to be explaining the methods used, and ever since starting this Mathematics journey this is something I've had issue with.  Some people find Mathematics hard to get into because of the certain barriers to entry, ie: the text won't fully explain what a variable is or (case in point) won't explain how to get from one step to the next. Often such a step is taken as "obvious", and I've always considered this as somewhat "elitist". With this assignment I've face-palmingly found myself falling into the same trap.

This is doubly interesting for me, as I actually do really enjoy going into lots of detail in explaining something I've worked on. So in future, I'll be mindful to explain more of my workings in plain English; or at least summarise them in plain English.

Linear Algebra

Blimey. That was a journey... I've always wanted to know more about mathematics in dimensions higher than 3. Turns out I should be careful what I wish for!

Given my background and prior knowledge of 3d transformations, I thought I might find this section rather easy. Though shortly after starting it, I was forced to think about what would constitute an orthonormal basis in four dimensions. Needless to say, this is not only unintuitive, but also impossible to imagine (and as a colleague quite correctly pointed out, impossible to draw!). So instead of relying on intuition, you rely on basic generalised properties of manipulation of bases. After that, you can work in any dimension you want!

Interestingly, amongst all this talk of linear transforms and bases, there was not one mention of cross products. Everything was done without the need for them, which is an eye-opener given the liberal scattering of cross products in my own transformation code!

Perhaps one of the most interesting things I looked at was a description of a basis in four dimensions that you go on to prove is actually representable in three dimensions. Obviously, it's not always possible to do, but this representation of higher dimensions in lower ones was something else I'd been interested in for a while. The 4D window on dimensionality has begun to open!

This section was really fun. It's a shame there is only one section on it this time around. Next up... the dreaded Analysis...