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I know many have experience with Gilbert Strang's Introduction to Linear Algebra textbook and course (http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebr...), but I thought it would be useful to mention them here. I've found his explanations to be very intuitive.

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Agreed, I bought the book and am doing the class as a "refresher". I put refresher in quotes because there is stuff in Strang's class that I know we didn't cover in my university class, notably SVD. Strang definitely has a way of really helping you deeply understand the concepts. I remember the subject pretty well but I don't think I understood it as well as I do now.

I don't know if Strang's approach would be good as an initial run through Linear Algebra, but it's a great refresher/enhancer (I read through it in grad school to prepare for prelims, back when I thought I was going to got for an applied mathematics PhD.)

What would be?

Maybe Khan academy?

https://www.khanacademy.org/math/linear-algebra

Kahn Academy is great for people with no access to educational materials -- that's why it was created. But it isn't material developed by professional or expert educators.

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