Applied Linear Algebra

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This textbook develops essential tools of linear algebra, aiming to impart both technique and contextual understanding. Applications and theory are intertwined, reinforcing each other to help students gain technical proficiency and an appreciation for the use of linear algebra in modern applied mathematics. It covers key topics such as Gaussian elimination, inner products, norms, eigenvalues, and singular values, suitable for both an in-depth first course or an application-driven second course. The second edition features updated and expanded applications, including numerical methods, dynamical systems, data analysis, and signal processing, while enhancing the pedagogical flow of core material. The text emphasizes conceptual connections between applications and underlying linear algebra techniques, enabling students to apply mathematical tools in routine contexts and adapt to unique problems. No prior knowledge of linear algebra is required, with single-variable calculus as the only prerequisite. However, some mathematical maturity is necessary to engage with the increasing abstraction of the subject. Equipped with the tools and concepts from this book, students will be prepared for further studies in differential equations, numerical analysis, data science, and statistics. The first author’s text on partial differential equations serves as an ideal companion, extending the linear mathematical methods developed here.