[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.