Strang's hand-wavy teaching style in my opinion kinda falls apart towards the later part of the course. I feel like the whole second half is kinda half baked. I didn't come away really having a good intuitive understanding of what the SVD was or why I should care about eigenvalues. I definitely think it's a good place to start though, but if you want something a little more organized I'd really recommend.
It's very clearly written and all the proofs are not too long nor too short. It pretty quickly goes through all the stuff Strang covers and moves on to more difficult things.
"Matrix Analysis and Applied Linear Algebra"
http://www.amazon.com/Matrix-Analysis-Applied-Algebra-Soluti...
It's very clearly written and all the proofs are not too long nor too short. It pretty quickly goes through all the stuff Strang covers and moves on to more difficult things.