Linear Algebra: A Pathway to Abstract Mathematics 3rd ed.

There is no mathematical ramp that will enable you to continuously inch your way higher and higher in mathematics. The climb calls for a ladder consisting of discrete steps designed to take you from one mathematical level to another. You are about to take an important step on that ladder, one that will take you to a plateau where mathematical abstraction abounds. Linear algebra rests on a small number of axioms (accepted rules, or "laws"), upon which a beautiful and practical theory emerges.