Hello Again, Linear Algebra: A Second Look at the Subject through a Collection of Exercises and Solutions

This book is for current linear algebra students looking to master the concepts of the subject, and for those who have taken it in the past looking for a refresher. It's an easy read which aims to illustrate concepts with examples and exercises.

Linear algebra is a grand subject. Because it is fundamentally different from any high school mathematics, and because of the wildly varying quality of instructors, not all students enjoy learning it. In either case, whether you loved it or hated it, it takes several passes to learn linear algebra to the point that it becomes one of your favorite tools, one of your favorite ways of thinking about practical problems.

This little textbook invites you on your second pass at linear algebra. Of course, your second pass may take place alongside your first pass. You may find this textbook particularly useful if you are studying for a test. Our goal is to take a step back from the mechanics of the subject with an eye towards gaining a larger view. A larger view, however, is achieved in small steps. We are not hoping for a big revelation but for a few small aha! moments. It simply takes time to put together the grand puzzle of linear algebra. You will get there, and the point, as the cliche goes, is to enjoy the ride.

Psychology in mathematics is everything. I chose the topics according to the impact I feel they would make on your relationship with linear algebra. The textbook's utmost goal is to make you feel positively about the subject. You will find that some topics are surprisingly simple, others surprisingly tough. Some topics have important applications, others have none at all. Some were well presented in your linear algebra course, others skipped altogether. However, I hope you will find that all topics bring you a little closer to the subject of linear algebra.