Applied Numerical Linear Algebra

Beautiful! Very simply, if you want to have an insight on linear algebraic procedures, and why this and that happens so and so, this is the book. Topic-wise, it is almost complete for a first treatment. Each chapter starts with a gentle introduction, building intuition and then gets into the formal material. The style is solid. Although talking about procedures, it also attempts to give some geometric intuition here and there. It helps. This is not a reference book though. You cannot find every important procedure.