"Theory and applications of linearity, including vectors, matrices, systems of linear equations, dot and cross products, determinants, linear transformations in Euclidean space, linear independence, bases, eigenvalues, eigenvectors, and diagonalization."

Sophomore-level textbook. " It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors."

By Jim Hefferon

"Overall, the aim of the textbook is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work." By W. Keith Nicholson.

"This text is used in the [Brown U.] honors course that emphasizes proofs. The book’s title suggests that it is not the typical approach to linear algebra even among those books that are more theoretical. For example, the concept of a basis is treated as more fundamental than the concept of linear independence, and linear transformations are introduced before solving systems of linear equations. Especially noteworthy is the motivation and development of determinants."