Axler and Strang are really very different books with very different intents. The most striking example is that Gaussian elimination is practically the first th

Axler and Strang are really very different books with very different intents. The most striking example is that Gaussian elimination is practically the first thing that Strang covers, but Axler doesn't cover it at all. I can't speak in general because I've only skimmed Strang, whereas I worked through nearly all of Axler. But if your interest in Linear Algebra is as preparation for quantum mechanics, then Axler is a great choice, perhaps even for a novice (though it does require a bit of mathematical maturity). Axler really hammers you with the idea that a matrix is just a way to represent a linear transformation, and that the numbers in the matrix depend on the basis you choose for the underlying vector space. This way of thinking is very helpful when you learn quantum mechanics. EDIT: Axler also has the advantage that it is short. Personally, I find it much easier to work independently through short math/physics books than long books.