FUNDAMENTALS OF LINEAR ALGEBRA (HB 2019) Hardcover

"Fundamentals of Linear Algebra stands apart from other books on the topic by offering a natural, unified approach, providing a more thorough understanding in under 250 pages compared to other texts that are often twice as long. For example, while most U.S. textbooks prove the existence of a basis only for finite-dimensional vector spaces, this book extends that proof to all vector spaces. Leveraging his expertise in algebraic geometry and commutative algebra, the author defines the dimension of a vector space using its Krull dimension. This simplifies many facts about bases in finite-dimensional spaces, making them direct outcomes of this definition. For instance, the replacement theorem becomes unnecessary, and it is immediately clear that any two bases of a finite-dimensional vector space will contain the same number of vectors. Furthermore, this dimension definition is equally applicable to nonlinear geometric objects."