This is an absolutely excellent book. I came at it before I had ever taken a linear class. The book develops the subject in a way that it seems a natural progression. I was never faced with a proof that seemed to be just number crunching; they all get at the very heart of what is at stake. I recently read back through it after taking a linear class, and I still come to a better understanding of the subject by looking through this. It is well worth your time. The only complaint I have with the book is that there are a lot of typos. It frequently refers back to the wrong problem number, and there are typos in the mathematics that could cause problems if you aren't keeping track of what is happening. (Ex: in the solution to 135, they forget to specify orthogonal projections, or in 145 they say that if y=Px then what is wanted is Uy=Px when it should actually read Uy=Ax) The text is written clearly enough you should be able to figure out what is happening, but if another edition comes out it would be worth upgrading