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 don't think that's really true. The book itself puts it much more simply and directly, at the very beginning in 'Preface for the Instructor':
"You are about to teach a course that will probably give students their second exposure to linear algebra."