linear algebra resources

Although our class is using Peter Lax's Linear Algebra and Its Applications, 2nd Edition, our professor suggested that I take a look at Sheldon Axler's Linear Algebra Done Right, 2nd Edition.  I have found that Chapter 6 ("Inner Product Spaces") to be very helpful in to read along with Chapter 7 ("Euclidean Structure) of Lax, particularly the section on linear functionals and adjoints, which has some concrete examples of each.  

I have only skimmed Chapter 7 ("Operators on Inner Product Spaces") of Axler, but it goes through the spectral theorem in a much more concrete way and I think will be helpful to read along with Chapter 6 ("Spectral Theory") of Lax.

Happily, both of these are available on Sheldon Axler's website as sample chapters.  I really like his book because it's written at a much more conversational and concrete level than Lax, and the proofs have more explanation as it is aimed towards undergraduates taking a second course in linear algebra.  Lax tends to be extremely terse, and as someone with less math background, Axler's book has turned out to be extremely helpful.  It also happily avoids (or at least postpones) the discussion of determinants to the end, which I appreciate since I still find determinants rather unintuitive.