Study HN: Linear Algebra 1, fortnight 2
Most of us are squeezing this into limited spare time - a packing problem in its own right - and several are working through all the exercises, so our pace has proven slower than a typical course would go. At this point, though, we should at least declare 1.2 and 1.3 done. Less than that is just embarrassing. If you made it past 1.4 long ago, good for you; please post some comments to goad the rest of us forward. If you're not on 1.4 yet, get your ass in gear! Here are a couple observations to entice you.
1.4 is about matrix multiplication, which would seem to be about as mechanical and shallow a topic as you could get. I was surprised at how deep Strang was able to make it. (But be aware that we're not reading Standard Strang, we're reading Hippie Strang. That's ISBN 0030105676.) I thought that mastering the element-wise way of multiplying two matrices was all you needed to have it down. But Strang doesn't want you to think of it that way; he even impedes that view. Instead, 1.4 takes the earlier theme of the "row picture" and "column picture" and develops it further by teaching the matrix product AB as a combination of the columns of A or (alternatively) the rows of B. This is the book's bias in general, to de-emphasize formal representations and focus on the meaning of the constructs instead.
The other point concerns the exercises for 1.4. I put them off for a while because I thought they would be rote. They're not. They're designed to trigger insights that don't come automatically from reading the text, and turn out to be surprisingly satisfying. I found myself alternating between "aha!" and "doh!" when completing them. Yeah, that says something about the obtuseness of the student, but more about the skill of the teacher. Clearly a lot of love was put into crafting those exercises. So so far, I'd say we lucked out in picking this book.
p.s. If this sounds like fun, you should join us. All you have to do is learn. And it would still be pretty easy to catch up.