[nx]

I usually can understand abstract concepts, but also need, or prefer, to work all the way from the bottom up, just to make sure it works like I think it does. I can't just believe something the teacher tells me, I have to prove it works that way, based on past knowledge. But it is necessary to be able to function in higher levels of abstraction, I understand matrix multiplication as a bunch of dot-products, not as sums of products of numbers, for example, and from that easily derives the need for equal number of columns/rows.