[mrcoder111]

I took a linear algebra course. Maybe I need to restudy but I would rather have links to exact chapters than reading the whole thing, as I don't see a direct path from the linear algebra I studied to the topology concepts and geometry here. Specifically there weren't any curves in linear algebra. Ex 4.10 and 4.11 here: http://planning.cs.uiuc.edu/node143.html

Are examples of things that are hard for me to understand. Especially that 2d picture in 4.11

[chongli]

You have to study quite a lot of linear algebra before you can tackle functional analysis, the subject which includes the study of topological vector spaces. I don't know anything about robotics, however, so I don't know how functional analysis would apply, if at all.

[tnecniv]

Functional analysis shows up all over the place. Everywhere you can take a Fourier transform, you can use functional analysis. For robotics, control theory and computer vision both come to mind.