I tried Strang, but I prefer books to lectures. I took an introductory course, but was left with "So what?" I plan to self-study over the summer for machine learning course in the fall.
I have worked a bit with Strang and I love the intiution that his lectures provide but I did not finish the full course :)
I initially wanted to suggest Linear Algebra from Foundation to Frontiers [1] as it had an accompanying book [2] from Edx, but I had no experience in that, so checked up a bit online and outside their course website, they had not so good reviews [3]. So I am providing the links for you to decide yourself. Another answer on quora [4] suggests Coding the Matrix from Coursera, which is supposed to be rigorous in algorithms with excellent assignments in real world applications. So may be that is your cup of tea.
I was in a similar situation. If you were left with a "So what" feeling then I imagine it would be difficult to plow through a general linear algebra book without having a feel for the end-game.
Since you already took an introductory course, why not just start studying machine learning directly and learn the little linear algebra you need on the side? How much more linear algebra do you really think you need? Don't be a Depth-First-Search learner ;-) [1]
Work yourself through on paper. Really helps. Jumping vectors into matrixes and vice versa I found fun. Then do the same thing at multi-dimension levels, should also be fun. Then you're there.
Edit: Maths, just study maths. Not meaning to a higher degree, but to enjoy it.
Isn't Linear algebra taught in the 10th grade? I remember I took linear algebra again in college since they don't have an AP test for it, but it was mostly the the same stuff. I remember getting an A in the class without too much studying since it was pretty much just using matrices.
I initially wanted to suggest Linear Algebra from Foundation to Frontiers [1] as it had an accompanying book [2] from Edx, but I had no experience in that, so checked up a bit online and outside their course website, they had not so good reviews [3]. So I am providing the links for you to decide yourself. Another answer on quora [4] suggests Coding the Matrix from Coursera, which is supposed to be rigorous in algorithms with excellent assignments in real world applications. So may be that is your cup of tea.
[1] https://www.edx.org/course/linear-algebra-foundations-fronti...
[2] http://ulaff.net/
[3] https://www.quora.com/Which-online-course-for-linear-algebra...
[4] https://www.quora.com/If-linear-algebra-is-so-important-for-...