I guess I just love this book. It's exactly as advertised: rigorous yet practical. What sets this book apart is that it'll make you fluent in rigorous mathematical notation, as a side-effect. You'll begin reading more advanced material after this. You'll be writing your matrixes in sigma notation in no-time!

On the whole, this covers what any other LA book does (could it be any different?). I think here and there it could have provided more proofs.The approach is always finite-dimensional.

It's a book geared for students having a matrix-oriented approach and yet wish to remain with a foot on the more mathy side of the learning experience, aiming at "the next level" of mathematical maturity. For maths and physics undergraduates, I guess.