"There is hardly any theory which is more elementary [than linear algebra], in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calculations with matrices." -Jean Dieudonné

Solutions to the 3rd edition of Linear Algebra Done Right, by Sheldon Axler.

• Chapter 1: Vector Spaces
• Chapter 2: Finite-Dimensional Vector Spaces
• Chapter 3: Linear Maps
• Chapter 4: Polynomials
• Chapter 5: Eigenvalues, Eigenvectors, and Invariant Subspaces
• Chapter 6: Inner Product Spaces
• Chapter 7: Operators on Inner Product Spaces

When I decided to go back and review linear algebra, I spent a decent amount of time looking at various options for a text and eventually settled on Axler's book (I had read parts of the 2nd edition in the summer before graduate school, and I remembered it being quite good). His approach to linear algebra is pretty polarizing, with many praising the book's more abstract approach and others criticizing it for his decision to defer use of the determinant until the end of the book. I happen to enjoy this style, and I think it really streamlines the presentation of linear algebra pedagogically. But I also understand this might not suit everyone's taste, and two good alternatives are the excellent books by Hoffman & Kunze and Friedberg et al.

It probably goes without saying, but this is not an appropriate book for a first encounter with linear algebra. The material won't stick unless you've studied the subject from the perspective of, e.g., Gilbert Strang's book (which approaches linear algebra from a more applied point-of-view and is also a great book).

The problems are, on the whole, excellent. However, a future edition might do well to trim some of the fat. Earlier editions of the book had fewer problems, but they were all well-chosen.