Matrices and Vector Spates

As the author implies this book is intended for a graduate course in linear algebra or for an honors course--which is exactly what it is intended for. I'm surprised I didn't hear of this book until the author happened to be my professor for linear algebra. Though we did not use his book for the class (We used Leon, sadly), I did an "honors option" and worked out of his book. I found it far more illuminating than Leon, who does not even develop the theory of determinants using permutations and instead adopts the typical (and far less interesting) Laplace expansion for determinants. The way this book is written, the reader should definitely be acquainted with basic function theory (injective, surjective, etc.), have a decent background in set theory, and be familiar with some terms from algebra (homomorphisms, isomorphisms, etc.). The problems range from simply computational to challenging proofs, with suggestions and answers in the back for a good majority. Overall, if you're looking for a pretty good preparation for graduate linear algebra or a senior-level linear algebra, this is a good text, because it really skips over all the applications in engineering and science that seem to clutter today's linear algebra textbooks.