Linear Algebra

This book is an introductory textbook in linear algebra. The authors begin with a primer on logic and set theory in the first two chapters. Functions are also covered early so that the core topic of linear transformations can be introduced near the beginning of the book and serve as a motivation to solving systems of equations. Next, Euclidean Spaces and functions between Euclidean Spaces are covered. This includes specific discussions on vectors and the standard basis, vector algebra, Pythagoras, and matrix transformations. Invertible Linear Transformations are then examined, along with Spaces without Geometry. This section includes a discussion of subspaces, linear independence, and change of basis. The authors then cover functions between spaces and geometry on vector spaces. Simplifying linear transformations is then discussed. The book concludes with two advanced chapters covering matrix theory and more general algebraic structures.