[dnautics]

I learned abstract linear algebra first, and didn't learn geometrical interpretations until I taught myself many years later so I could write an asteroids clone in svg.

I don't think it was a pedagogically a problem, except I couldn't bring myself to care about matrices when I was learning them... It was very easy to take my abstract knowledge and apply it, and for me it might have been harder the other way around.

In retrospect a hybrid applied/theoretical topic (like reed Solomon encoding and recovery) might have perked me up. But I might have also been a strange case.

[akater]

If by “abstract” linear algebra you mean “course that starts with the definition of vector space”, then it is geometric enough in the sense Artin talks about.

It is pedagogically a problem for people who ask questions like the one in topic. But it can also be a problem when one encounters bilinear form and linear operator in practice but can't distingish between the two. I can't think of a specific example but I was asked once about some problem (in electrical engineering, iirc) where the source of confusion was this; some transformations of a (square) matrix were natural while others were not.

Some people feel strongly about the topic—mostly those with “pure math” inclinations.