| LEC # | Topics | Readings |
|---|---|---|
| 1 | The Geometry of Linear Equations | 1.1-2.1 |
| 2 | Elimination with Matrices | 2.2-2.3 |
| 3 | Matrix Operations and Inverses | 2.4-2.5 |
| 4 | LU and LDU Factorization | 2.6 |
| 5 | Transposes and Permutations | 2.7 |
| 6 | Vector Spaces and Subspaces | 3.1 |
| 7 | The Nullspace: Solving Ax = 0 | 3.2 |
| 8 | Rectangular PA = LU and Ax = b | 3.3-3.4 |
| 9 | Row Reduced Echelon Form | 3.3-3.4 |
| 10 | Basis and Dimension | 3.5 |
| 11 | The Four Fundamental Subspaces | 3.6 |
| 12 | Exam 1: Chapters 1 to 3.5 | |
| 13 | Graphs and Networks | 8.2 |
| 14 | Orthogonality | 4.1 |
| 15 | Projections and Subspaces | 4.2 |
| 16 | Least Squares Approximations | 4.3 |
| 17 | Gram-Schmidt and A = QR | 4.4 |
| 18 | Properties of Determinants | 5.1 |
| 19 | Formulas for Determinants | 5.2 |
| 20 | Applications of Determinants | 5.3 |
| 21 | Eigenvalues and Eigenvectors | 6.1 |
| 22 | Exam Review | |
| 23 | Exam 2: Chapters 1-5 | |
| 24 | Diagonalization | 6.2 |
| 25 | Markov Matrices | 8.3 |
| 26 | Fourier Series and Complex Matrices | 8.5, 10.2 |
| 27 | Differential Equations | 6.3 |
| 28 | Symmetric Matrices | 6.4 |
| 29 | Positive Definite Matrices | 6.5 |
| 30 | Matrices in Engineering | 8.1 |
| 31 | Singular Value Decomposition | 6.7 |
| 32 | Similar Matrices | 6.6 |
| 33 | Linear Transformations | 7.1-7.2 |
| 34 | Choice of Basis | 7.3-7.4 |
| 35 | Exam Review | |
| 36 | Exam 3: Chapters 1-8 (8.1, 2, 3, 5) | |
| 37 | Fast Fourier Transform | 10.3 |
| 38 | Linear Programming | 8.4 |
| 39 | Numerical Linear Algebra | 9.1-9.3 |
| 40 | Final Exams |
Table of Contents
Study Materials
Readings
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The readings are assigned in: Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2009. ISBN: 9780980232714.
1. Introduction to Vectors
1.1 Vectors and Linear Combinations
1.2 Lengths and Dot Products
2. Solving Linear Equations
2.1 Vectors and Linear Equations
2.2 The Idea of Elimination
2.3 Elimination Using Matrices
2.4 Rules for Matrix Operations
2.5 Inverse Matrices
2.6 Elimination = Factorization: A = LU
2.7 Transposes and Permutations
3. Vector Spaces and Subspaces
3.1 Spaces of Vectors
3.2 The Nullspace of A: Solving Ax = 0
3.3 The Rank and the Row Reduced Form
3.4 The Complete Solution to Ax = b
3.5 Independence, Basis, and Dimension
3.6 Dimensions of the Four Subspaces
4. Orthogonality
4.1 Orthogonality of the Four Subspaces
4.2 Projections
4.3 Least Squares Approximations
4.4 Orthogonal Bases and Gram-Schmidt
5. Determinants
5.1 The Properties of Determinants
5.2 Permutations and Cofactors
5.3 Cramer's Rule, Inverses, and Volumes
6. Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues
6.2 Diagonalizing a Matrix
6.3 Applications to Differential Equations
6.4 Symmetric Matrices
6.5 Positive Definite Matrices
6.6 Similar Matrices
6.7 The Singular Value Decomposition (SVD)
7. Linear Transformations
7.1 The Idea of a Linear Transformation
7.2 The Matrix of a Linear Transformation
7.3 Change of Basis
7.4 Diagonalization and the Pseudoinverse
8. Applications
8.1 Matrices in Engineering
8.2 Graphs and Networks
8.3 Markov Matrices and Economic Models
8.4 Linear Programming
8.5 Fourier Series: Linear Algebra for Functions
8.6 Computer Graphics
9. Numerical Linear Algebra
9.1 Gaussian Elimination in Practice
9.2 Norms and Condition Numbers
9.3 Iterative Methods for Linear Algebra
10. Complex Vectors and Complex Matrices
10.1 Complex Numbers
10.2 Hermitian and Unitary Matrices
10.3 The Fast Fourier Transform