note that this is just part 1 of 4.
(I am assuming you didn't read all four parts, because that material would have to be covered impressively quickly to fit in 20 minutes)
Well, 20 minutes was perhaps an exaggeration, but in our first lecture we covered everything up to the end of part 2 and most of part 3. I think in the second lecture we did a significant amount of part 4, but then we went in a different direction.
We certainly did changes of basis and arbitrary dimensional rotation in our first lecture. We didn't do quaternions, and in fact never did in the context of these sorts of things.
Of course, we had done basic vectors and matrices in secondary school - we certainly knew how to multiply N dimensional matrices, and were expected to invert 2-D matrices by hand and compute the determinant of 3-D matrices. They were on the final exam.
We certainly did changes of basis and arbitrary dimensional rotation in our first lecture. We didn't do quaternions, and in fact never did in the context of these sorts of things.
Of course, we had done basic vectors and matrices in secondary school - we certainly knew how to multiply N dimensional matrices, and were expected to invert 2-D matrices by hand and compute the determinant of 3-D matrices. They were on the final exam.