Linear Algebra
Version 0 (11/15/2017)
- Introduction to Matrices
- Elementary Row Operations
- Gaussian-Jordan Elimination
- Solutions of Systems of Linear Equations
- Linear Combination and Linear Independence
- Nonsingular Matrices
- Inverse Matrices
- Subspaces in $\R^n$
- Bases and Dimension of Subspaces in $\R^n$
- General Vector Spaces
- Subspaces in General Vector Spaces
- Linearly Independency of General Vectors
- Bases and Coordinate Vectors
- Dimensions of General Vector Spaces
- Linear Transformation from $\R^n$ to $\R^m$
- Linear Transformation Between Vector Spaces
- Orthogonal Bases
- Determinants of Matrices
- Computations of Determinants
- Introduction to Eigenvalues and Eigenvectors
- Eigenvectors and Eigenspaces
- Diagonalization of Matrices
- The Cayley-Hamilton Theorem
- Dot Products and Length of Vectors
- Eigenvalues and Eigenvectors of Linear Transformations
- Jordan Canonical Form