As someone who worked their way through Strang (we did a little study group and did the homework assigned to some class at Rutgers), I'd love it if someone could take a moment to explain what they like so much about Axler. I've tried a couple times to slog my way through Axler and had not much success.
I’m not in the target audience and have neither learned nor taught from Axler’s book, so I can’t tell you precisely what people like about it, but it is aimed at pure math undergraduates who are interested in using linear algebra in much more abstract contexts, and focuses more on proofs than many introductory linear algebra textbooks.
Not a contradiction. Their first exposure would have been something like multivariable Calculus. So students have seen matrices, but they were magic, unmotivated, and probably didn't make much sense except in a "here is the formula to memorize" kind of way.
Axler tries to teach students how to understand linear algebra.
If all that you want to do is use it, the prospect of that understanding may not be very motivating.
I was commenting about what Axler is, and not comparing it to anything else.
My point is that the comment that you quoted from the preface in no way changes the fact that the book's point is to convey an understanding of linear algebra that is primarily of interest to people going on in math.
Now I happen to think it is the right way to understand linear algebra and is how people in other fields should think about it. Because it is easier to figure out again if you've not done it in a while. But this point of view is primarily going to motivate would be mathematicians.
You don’t think this book is aimed at pure mathematics students?
It’s certainly not aimed at numerical analysis students, or engineering students, or physics students. (Which isn’t to say that those students can’t take pure math courses if they want.)
I mean in the context of Strang. I don't think Strang is aimed strictly at, say, engineering students. To me, the difference is the starting point, more than anything else.
As far as I can tell Strang’s target audience is something like: most undergraduates at MIT who didn’t already learn the subject before arrival, except the pure math students who are likely to substitute a more theoretical course (18.700 or 18.701 vs. 18.06).
Right. Each is aimed at somewhat different audiences. We're undoubtedly getting into some pretty fine hairsplitting, the thing I was whining about is 'pure maths students' and 'everyone else' is not an accurate way to describe them.
I have both Axler and Strang. I learned from Axler but occasionally use Strang as a reference. I find that Axler emphasizes the algebra part of linear algebra while Strang emphasizes the linear part. One isn't better than the other but one might make more sense to different people.
Axler avoids determinants with a passion. For good reason, too, because they are not helpful in understanding how spaces interact. I forget how Strang proves the spectral theorem but compared to Lax the pedagogy could not be more different. Determinants are really nice tools for short proofs, but not helpful in understanding. But Axler is the way you want to think about linear algebra as a practitioner.
Axler is easier to digest if you have some familiarity with the tools and the jargon but hated/forgot everything in your college linear algebra course.
A (very imperfect) analogy might be something like the GoF book vs Peter Norvig's essay on design patterns.
