If I did a write up explaining the difference between complex number representation of vectors vs Matrix/Linear algebra representations would anyone be interested in reading that.

I feel it would be useful to explain why and how multiplication is different between the two and why division on matrix vectors is forbidden but allowed in complex form and the repercussions of that.

Might also be useful to go into some explanation as to how to intuitively know when to use one or the other (something even i struggle with from time to time).