Introducing students to a subject that lies at the foundations of modern mathematics, physics, statistics, and many other disciplines, "Linear A Geometric Approach" should appeal to science and engineering students as well as mathematics students making the transition to more abstract advanced courses. One of the main aims of this text - aside from presenting the standard computational aspects - is to help students learn to think about mathematical concepts and to write rigorous mathematical arguments. The authors do not presuppose any exposure to vectors or vector algebra.
Great book, reading through it a second time 7 years later and just as easy to read through and understand concepts. The authors attempt to make it read like a novel, so no need to stop and do exercises to complete understanding (although this obviously helps).