[btilly]

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.

[pvg]

I didn't say there was some contradiction. I just don't think the key difference between Strang and Axler is really the degree of mathsiness.

[btilly]

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.

[pvg]

and not comparing it to anything else.

Sure, but the topic is 'Given Strang, what's the deal with Axler'. It's a perfectly sensible question in its own right.