Sadly the list is missing my favorite math book, "Linear Algebra Done Right" by Sheldon Axler. It's an absolute must if you are learning linear algebra and want a deep understanding of it.
Rather than make you grind through mechanical operations on matrices, as most books do, this book takes a coordinate-free algebraic approach and does an amazing number of things with it, cutting directly to the chief insights. There are ninja proofs in this book, 4 lines long, showing some deep and useful thing about linear algebra that other books would spend pages proving in a very verbose and uninsightful way.
Rather than make you grind through mechanical operations on matrices, as most books do, this book takes a coordinate-free algebraic approach and does an amazing number of things with it, cutting directly to the chief insights. There are ninja proofs in this book, 4 lines long, showing some deep and useful thing about linear algebra that other books would spend pages proving in a very verbose and uninsightful way.