| |
| |
| |
| Vectors | |
| |
| |
| |
| The Geometry and Algebra of Vectors | |
| |
| |
| |
| Length and Angle: The Dot Product | |
| |
| |
| Exploration: Vectors and Geometry | |
| |
| |
| |
| Lines and Planes | |
| |
| |
| Exploration: The Cross Product | |
| |
| |
| |
| Applications | |
| |
| |
| |
| Review | |
| |
| |
| |
| Systems of Linear Equations | |
| |
| |
| |
| Introduction to Systems of Linear Equations | |
| |
| |
| Exploration: Lies My Computer Told Me | |
| |
| |
| |
| Direct Methods for Solving Linear Systems | |
| |
| |
| Exploration: Partial Pivoting | |
| |
| |
| Exploration: An Introduction to the Analysis of Algorithms | |
| |
| |
| |
| Spanning Sets and Linear Independence | |
| |
| |
| |
| Applications | |
| |
| |
| |
| Iterative Methods for Solving Linear Systems | |
| |
| |
| |
| Review | |
| |
| |
| |
| Matrices | |
| |
| |
| |
| Matrix Operations' | |
| |
| |
| |
| Matrix Algebra | |
| |
| |
| |
| The Inverse of a Matrix | |
| |
| |
| |
| The LU Factorization | |
| |
| |
| |
| Subspaces, Basis, Dimension, and Rank | |
| |
| |
| |
| Introduction to Linear Transformations | |
| |
| |
| |
| Applications | |
| |
| |
| |
| Review | |
| |
| |
| |
| Eigenvalues and Eigenvectors | |
| |
| |
| |
| Introduction to Eigenvalues and Eigenvectors | |
| |
| |
| |
| Determinants | |
| |
| |
| Exploration: Geometric Applications of Determinants | |
| |
| |
| |
| Eigenvalues and Eigenvectors of n � n Matrices | |
| |
| |
| |
| Similarity and Diagonalization | |
| |
| |
| |
| Iterative Methods for Computing Eigenvalues | |
| |
| |
| |
| Applications and the Perron-Frobenius Theorem | |
| |
| |
| |
| Review | |
| |
| |
| |
| Orthogonality | |
| |
| |
| |
| Orthogonality in Rn | |
| |
| |
| |
| Orthogonal Complements and Projections | |
| |
| |
| |
| The Gram-Schmidt Process and the QR Factorization | |
| |
| |
| Exploration: The Modified QR Factorization | |
| |
| |
| Exploration: Approximating Eigenvalues with the QR Algorithm | |
| |
| |
| |
| Orthogonal Diagonalization of Symmetric Matrices | |
| |
| |
| |
| Applications | |
| |
| |
| |
| Review | |
| |
| |
| |
| Vector Spaces | |
| |
| |
| |
| Vector Spaces and Subspaces | |
| |
| |
| |
| Linear Independence, Basis, and Dimension | |
| |
| |
| Exploration: Magic Squares | |
| |
| |
| |
| Change of Basis | |
| |
| |
| |
| Linear Transformations | |
| |
| |
| |
| The Kernel and Range of a Linear Transformation | |
| |
| |
| |
| The Matrix of a Linear Transformation | |
| |
| |
| Exploration: Tilings, Lattices, and Crystallographic Restriction | |
| |
| |
| |
| Applications | |
| |
| |
| |
| Review463 | |
| |
| |
| |
| Distance and Approximation | |
| |
| |
| |
| Inner Product Spaces | |
| |
| |
| Exploration: Vectors and Matrices with Complex Entries | |
| |
| |
| |
| Norms and Distance Functions | |
| |
| |
| |
| Least Squares Approximation | |
| |
| |
| |
| The Singular Value Decomposition | |
| |
| |
| |
| Applications | |
| |
| |
| |
| Review | |
| |
| |
| |
| Key Definitions and Concepts | |
| |
| |
| |
| Theorems | |