Back to the class
Course definition: Systems of linear equations, matrices, vector spaces, inner products, linear transformations, determinants, and eigenvalues. (from here)
- Chapter 1
- Section 1-Systems of Linear Equations
- Section 2-Row Reduction and Echelon Forms
- Section 3-Vector Equations
- Section 4-The Matrix Equation $Ax=\textbf{b}$
- Section 5-Solution Sets of Linear Systems
Section 6-Applications of Linear Systems- Section 7-Linear Independence
- Section 8-Introduction to Linear Transformations
- Section 9-The Matrix of a Linear Transformation
Section 10-Linear Models in Business, Science, and Engineering
- Chapter 2
- Section 1-Matrix Operations
- Section 2-The Inverse of a Matrix
- Section 3-Characterizations of Invertible Matrices
- Section 4-Partitioned Matrices
- Section 5-Matrix Factorizations
Section 6-The Leontief Input-Output ModelSection 7-Applications to Computer GraphicsSection 8-Subspaces of $\mathbb{R}^n$Section 9-Dimension and Rank
- Chapter 3
- Section 1-Introduction to Determinants
- Section 2-Properties of Determinants
- Section 3-Cramer's Rule, Volume, and Linear Transformations
- Chapter 4
- Section 1-Vector Spaces and Subspaces
- Section 2-Null Spaces,Column Spaces, and Linear Transformations
- Section 3-Linear Independent Sets; Bases
- Section 4-Coordinate Systems
- Section 5-The Dimension of a Vector Space
- Section 6-Rank
- Section 7-Change of Basis
Section 8-Applications to Difference EquationsSection 9-Applications to Markov Chains
- Chapter 5
- Section 1-Eigenvectors and Eigenvalues
- Section 2-The Characteristic Equation
- Section 3-Diagonalization
- Section 4-Eigenvectors and Linear Transformations
- Section 5-Complex Eigenvalues
Section 6-Discrete Dynamical SystemsSection 7-Applications to Differential EquationsSection 8-Iterative Estimates for Eigenvalues
- Chapter 6
- Section 1-Inner Product, Length, and Orthogonality
- Section 2-Orthogonal Sets
- Section 3-Orthogonal Projections
- Section 4-The Gram-Schmidt Process
- Section 5-Least-Squares Problems
Section 6-Applications to Linear ModelsSection 7-Inner Product Spaces- Section 8-Applications of Inner Product Spaces
