This textbook develops the essential tools of linear algebra with the goal of imparting
technique alongside contextual understanding. Applications go hand-in-hand with theory each
reinforcing and explaining the other. This approach encourages students to develop not only the
technical proficiency needed to go on to further study but an appreciation for when why and
how the tools of linear algebra can be used across modern applied mathematics.Providing an
extensive treatment of essential topics such as Gaussian elimination inner products and norms
and eigenvalues and singular values this text can be used for an in-depth first course or an
application-driven second course in linear algebra. In this second edition applications have
been updated and expanded to include numerical methods dynamical systems data analysis and
signal processing while the pedagogical flow of the core material has been improved.
Throughout the text emphasizes the conceptual connections between each application and the
underlying linear algebraic techniques thereby enabling students not only to learn how to
apply the mathematical tools in routine contexts but also to understand what is required to
adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to
approach this text with single-variable calculus as the only formal prerequisite. However the
reader will need to draw upon some mathematical maturity to engage in the increasing
abstraction inherent to the subject. Once equipped with the main tools and concepts from this
book students will be prepared for further study in differential equations numerical analysis
data science and statistics and a broad range of applications. The first author¿s text
Introduction to Partial Differential Equations is an ideal companion volume forming a natural
extension of the linear mathematical methods developed here.
