Linear Equations in Linear Algebra
Systems of Linear Equations
Row Reduction and Echelon Form
Vector Equations
The Matrix Equation Ax->=b->
Solution Sets of Linear Systems
Applications of Linear Systems
Linear Independence
Introduction to Linear Transformations
The Matrix of a Linear Transformation
Matrix Algebra
Matrix Operations
The Inverse of a Matrix
Characterizations of Invertible Matrices
Subspaces of Rn
Dimension and Rank
Determinants
Introduction to Determinants
Properties of Determinants
Cramer's Rule, Volume, and Linear Transformations
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
The Characteristic Equation
Diagonalization
Eigenvalues and Linear Transformations
Complex Eigenvalues
Discrete Dynamical Systems
Vector Spaces
Vector Spaces and Subspaces
Null Spaces, Column Spaces, and Linear Transformations
Linearly Independent Sets; Bases
Coordinate Systems
The Dimension of a Vector Space
Rank
Change of Basis
Applications to Difference Equations
Applications to Markov Chains
Orthogonality and Least Squares
Inner Products Length, and Orthogonality
Orthogonal Sets
Orthogonal Projections
The Gram-Schmidt Process
Least-Squares Problem
Inner Product Spaces
Symmetric Matrices and Quadratic Forms
Diagonalization of Symmetric Matrices
Quadratic Forms
The Singular Value Decomposition