Table of Contents: “…5.2 The Characteristic Equation -- 5.3 Diagonalization -- 5.4 Eigenvectors and Linear Transformations -- 5.5 Complex Eigenvalues -- 5.6 Discrete Dynamical Systems -- 5.7 Applications to Differential Equations -- 5.8 Iterative Estimates for Eigenvalues -- Supplementary Exercises -- Chapter 6 Orthogonality and Least Squares -- INTRODUCTORY EXAMPLE: The North American Datum and GPS Navigation -- 6.1 Inner Product, Length, and Orthogonality -- 6.2 Orthogonal Sets -- 6.3 Orthogonal Projections -- 6.4 The Gram-Schmidt Process -- 6.5 Least-Squares Problems -- 6.6 Applications to Linear Models -- 6.7 Inner Product Spaces -- 6.8 Applications of Inner Product Spaces -- Supplementary Exercises -- Chapter 7 Symmetric Matrices and Quadratic Forms -- INTRODUCTORY EXAMPLE: Multichannel Image Processing -- 7.1 Diagonalization of Symmetric Matrices -- 7.2 Quadratic Forms -- 7.3 Constrained Optimization -- 7.4 The Singular Value Decomposition -- 7.5 Applications to Image Processing and Statistics -- Supplementary Exercises -- Chapter 8 The Geometry of Vector Spaces -- INTRODUCTORY EXAMPLE: The Platonic Solids -- 8.1 Affine Combinations -- 8.2 Affine Independence -- 8.3 Convex Combinations -- 8.4 Hyperplanes -- 8.5 Polytopes -- 8.6 Curves and Surfaces -- Appendixes -- A Uniqueness of the Reduced Echelon Form -- B Complex Numbers -- Glossary -- Photo Credits…”