A Modern Introduction to Linear Algebra

This text provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. It develops key concepts in the context of Euclidean n-space, explains the theory of matrices, and explores the differences between finite- and infinite-dimensional vector spaces. The book also covers the algebra and matrix representation of linear transformations. The author reviews basic mathematical tools in the appendices, presents proofs for nearly all results, and includes a host of examples and exercises, some of which reflect the various disciplines that use linear algebra. A solutions manual is available for qualifying instructors.