Beschreibung:
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.
Preface.- 1. Linear Algebraic Systems.- 2. Vector Spaces and Bases.- 3. Inner Products and Norms.- 4. Minimization and Least Squares Approximation.- 5. Orthogonality.- 6. Equilibrium.- 7. Linearity.- 8. Eigenvalues.- 9. Linear Dynamical Systems.- 10. Iteration of Linear Systems.- 11. Boundary Value Problems in One Dimension.- References.- Index.