This book presents the basic ideas of matrix and linear algebra in such a way that users from diverse backgrounds (who have had some exposure to calculus) will understand, by utilizing both algebraic and geometric reasoning. A spiral approach gradually introduces the abstract foundations of the topics involved—linear combination, closure, subspaces, linear independence/dependence, and bases. Opportunities for a variety of applications, and the optional use of MATLAB, provide hands-on explorations of computations and concepts. Chapter topics include matrices, linear systems and their solutions, Eigen information, vector spaces, inner product spaces, and linear transformations. For individuals who want to learn abstract concepts and deal with a wide variety of applications that can be drawn from fields such as physics, chemistry, biology, geology, economics, engineering, computer science, psychology, and sociology.