Edit: Thank you plinkplonk and acangiano. I'll stick with Strang for the time being then. Any recommendations for Real Analysis? The "Baby Rudin" looks to be just a bit out of my range.
A complete novice should go for Strang. Axler says upfront (in the preface iirc it has been a while since I worked through it) his book is intended as the second Linear Algebra book and assumes you have a base in Linear Algebra (matrix manipulations and so forth) already. Axler depends more on a classical "theorems and proofs" approach. Strang doesn't involve proofs etc and is more ocncerned with funamental operations and building intuition and so (imo) is more suited to the complete beginner.
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.