Laker Newhouse

I used this book for a second course in Linear Algebra (MIT 18.700) and loved it. The section on eigenvalues and inner products spaces were my favorites, but the whole book is a masterpiece. The print is high-quality, so I found that I could read it for longer than more bland black-and-white textbooks. It is fairly advanced, and it assumes that you can do basic proofs. You'd be find even if you were just starting with proofs, though, as long as you did a few exercises per section to make sure that you understand the material. The MIT 18.700 problem sets were a nice complement to the book's exercises, too. Linear Algebra Done Right is amazing!