Linear Algebra
Lecture Schedule based on Lay – Linear Algebra and Its Applications 3rd Edition
| Section | Lectures | Topic |
| 1.1 | 1 | Systems of Linear Equations |
| 1.2 | 1 | Row Reduction and Echelon Forms |
| 1.3 | 0.5 | Vector Equations |
| 1.4 | 1 | The Matrix Equation Ax = b |
| 1.5 | 1 | Solution Sets of Linear Systems |
| 1.6 | 0.5 | Applications of Linear Systems |
| 1.7 | 1 | Linear Independence |
| 1.8 | 0.5 | Introduction to Linear Transformations |
| 1.9 | 1 | The Matrix of a Linear Transformation |
| 2.1 | 1 | Matrix Operations |
| 2.2 | 1 | The Inverse of a Matrix |
| 2.3 | 0.5 | Characterizations of Invertible Matrices |
| 2.5 | 0.5 | Matrix Factorizations |
| 4.1 | 1 | Vector Spaces and Subspaces |
| 4.2 | 1 | Null Spaces, Column Spaces and Linear Transformations |
| 4.3 | 0.5 | Linearly Independent Sets; Bases |
| 4.5 | 0.5 | The Dimension of a Vector Space |
| 4.6 | 0.5 | Rank |
| 4.4 | 0.5 | Coordinate Systems |
| 4.7 | 1.5 | Change of Basis |
| 3.1 | 0.5 | Introduction to Determinants |
| 3.2 | 1 | Properties of Determinants |
| 3.3 | 0.5 | Cramer’ s Rule ; Volume and Linear Transformations |
| 5.1 | 1 | Eigenvectors and Eigenvalues |
| 5.2 | 1 | The Characteristic Equation |
| 5.3 | 0.5 | Diagonalization |
| 6.1 | 1 | Inner Product , Length and Orthogonality |
| 6.2 | 0.5 | Orthogonal Sets |
| 6.3 | 1 | Orthogonal Projections |
| 6.4 | 0.5 | The Gram-Schmidt Process |
| 6.5 | 0.5 | Least- Squares Problems |
| 7.1 | 1 | Diagonalization of Symmetric Matrices |
List of Topics for MATLAB laboratories:
1. Introduction to MATLAB
2. Systems of Linear Equations and Floating -Point Errors
3. Matrix Algebra
4. Elementary Row Operations and LU -Factorization
5. Linear Dependence, Column Space, Null Space, and Bases
6. Change of Basis and Coordinate Transformations
7. Eigenvalues and Determinants
8. Orthogonality and Least Squares
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