This acclaimed theorem-proof text presents a careful treatment of the principal topics of linear algebra. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. Applications to such areas as differential equations, economics, geometry, and physics appear throughout, and can be included at the instructor?s discretion. This book is especially suited to a second course in linear algebra that emphasizes abstract vector spaces, although it can be used in a first course with a strong theoretical emphasis. Updates to the 5th Edition include revised proofs of some theorems, additional examples, and new exercises. Also new in this revision are online solutions for selected theoretical exercises, accessible by short URLs at point-of-use. FeaturesRevised - A streamlined presentation, with clarified exposition informed by extensive reviews from instructors. Revised - Proofs of some theorems have been revised for further clarification. New - Additional examples and exercises throughout. New - Online solutions to selected theoretical exercises in each section of the book: oThese exercises each have their exercise number printed within a gray box, and the last sentence of each of these exercises gives a short URL for its online solution. New - Four new applications available online of the content in Sections 2.3, 5.3, 6.5, and 6.6. Short URLs at point-of-use provide easy access to this material.