And how much calculus is required to have a chance at understanding the material?
It might be nice to have some study groups in the bay area for people looking to get into this with a regular schedule.
It can be found here: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
Assuming no class is available, depending on how deeply you want to learn the subject, linear algebra is fairly accessible. It sounds like the introductory level stuff (University 200 level) is what is recommended in that article, so the good news is you don't need a class to learn it.
I don't think not having calculus would prevent learning it at this level. Personally I'd just look at reviews for linear algebra textbooks on Amazon and buy the best one. One thing I often do when trying to learn a subject on my own is a go to the University bookstore to figure out what materials I should start with.
Then just read the chapters and work the sample problems. When doing any matrix manipulation by hand (boring, but good to verify and help internalize understanding) it's easy to use that software to check results.
Basic linear algebra is one of the easier mathematics to teach one's self.
What kind of non-position are you talking about?
At least here in Germany, there's absolutely no problem with attending a linear algebra lecture as a guest. Just ask the lecturer whether it's okay for him/her, and everything is fine.
But of course, you need to be close to a university with decent linear algebra lectures, have enough time and so on. That's harder.
So all you need is a university that provides natural sciences. I can't imagine such a university being hard to find.