What is the significance of abstract linear algebra in machine learning/computer vision research?
In my experience (YMMV) linear algebra is very much used as a tool in Machine Learning and Computer Vision, with little interest in the underlying mathematics.

That said, you'll need a more mathematical understanding than, say, a games programmer or a basic researcher in the natural sciences. Basically you'll need to know enough to take a method like PCA apart and put it back together again, but you don't need to worry about your matrices containing anything other than real values. 

It sounds like this course is starting off deeper and more general than you want, but the list of topics suggests that you are moving in the right direction. So long as some attention is given to how to translate the mathematical methods into the computer. It's one thing to suggest that an SVD decomposition exists, and another to actually compute it.

The deep mathematical understanding won't hurt, but there's no guarantee that all of it will be useful to you.