Introductory Linear Algebra / I: |
Linear Equations and Matrices / 1: |
Linear Systems |
Matrices |
Dot Product and Matrix Multiplication |
Properties of Matrix Operations |
Graph Theory (Optional) |
Solutions of Linear Systems of Equations |
Electrical Circuits (Optional) |
Markov Chains (Optional) |
The Inverse of a Matrix |
Linear Economic Models (Optional) |
Wavelets (Optional) |
LU-Factorization (Optional) |
Determinants / 2: |
Definition and Properties |
Cofactor Expansion and Applications |
Determinants from a Computational Point of View |
Vectors in R2 and R3 / 3: |
Vectors in the Plane |
N-Vectors |
Introduction to Linear Transformations |
Computer Graphics |
Computer Graphics (Optional) |
Cross Products in R3 (Optional) |
Lines and Planes |
Real Vector Spaces / 4: |
Subspaces |
Linear Independence |
Basis and Dimension |
Homogeneous Systems |
The Rank of a Matrix and Applications |
Coordinates and Change of Basis |
Orthonormal Bases in Rn |
QR-Factorization (Optional) |
Orthogonal Complements |
Least Squares (Optional) |
Eigenvalues and Eigenvectors / 5: |
Diagonalization and Similar Matrices |
Diagonalization and Symmetric Matrices |
Linear Transformations and Matrices / 6: |
Definition and Examples |
The Kernel and Range of a Linear Transformation |
The Matrix of a Linear Transformation |
Cumulative Review of Part I |
OTHER APPLICATIONS / II: |
Linear Programming / 7: |
The Linear Programming Problem |
Geometric Solution |
The Simplex Method |
Duality |
The Theory of Games |
Applications of Eigenvalues and Eigenvectors / 8: |
The Fibonacci Sequence |
Differential Equations (Calculus Required) |
Dynamical Systems (Calculus Required) |
Intro to Fractals |
Quadratic Forms |
Conic Sections |
Quadric Surfaces |
Introduction to MATLAB / Appendix A: |
Complex Numbers / Appendix B: |
Complex Numbers in Linear Algebra |
Further Directions / Appendix C: |
Inner Product Spaces (Calculus Required) |
Composite and Invertible Linear Transformations |
Answers to Odd-Numbered Exercises and Chapter Tests |
Index |
Introductory Linear Algebra / I: |
Linear Equations and Matrices / 1: |
Linear Systems |
Matrices |
Dot Product and Matrix Multiplication |
Properties of Matrix Operations |