1. What is a Matrix?#30, Linear Transformations and Their Matrices |
7.1 The Idea of a Linear Transformation 7.2 The Matrix of a Linear Transformation (*) 1.3 Matrices (new to 4th edition) (*) |
2. Linear Equations#1: The Geometry of Linear Equations#2: Elimination with Matrices |
2.1 Vectors and Linear Equations 2.2 The Idea of Elimination |
3. Matrix Multiplications#3: Multiplication and Inverse MatricesHomework 3 |
2.4 Rules for Matrix Operations 2.5 Inverse Matrices (*) 7.2 The Matrix of a Linear Transformation (Products AB match...) (*) |
4. LU (Gauss-Jordan) and Inverses#4: Factorization into A = LUHomework 4, hw4.m |
2.3 Elimination Using Matrices 2.6 Elimination = Factorization: A = LU |
5. Orthogonal Matrices, Permutations#5: Transposes, Permutations, Spaces R^n#17: Orthogonal Matrices and Gram-Schmidt (*) Homework 5, hw5.m |
2.7 Transposes and Permutations |
6. Column Space and Kernel#6: Column Space and NullspaceHomework 6 |
3.1 Spaces of Vectors 3.2 The Nullspace of A: Solving Ax = 0 |
7. Row Reduced Form#7: Solving Ax = 0: Pivot Variables, Special Solutions#8: Solving Ax = b: Row Reduced Form R (*) Homework 7, hw7.m |
3.2 The Nullspace of A: Solving Ax = 0 3.3 The Rank and the Row Reduced Form |
8. Subspaces#9: Independence, Basis, and Dimension#10: The Four Fundamental Subspaces #13: Quiz 1 Review (*) Homework 8 |
3.5 Independence, Basis and Dimension 3.6 Dimensions of the Four Subspaces |
9. Projections#14: Orthogonal Vectors and Subspaces (*)#15: Projections onto Subspaces Homework 9 |
4.2 Projections |
10. Least Squares#16: Projection Matrices and Least SquaresHomework 10 |
4.3 Least Squares Approximations (*) |
11. Least Squares and Likelihood |
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12.QR Decomposition#17: Orthogonal Matrices and Gram-Schmidt |
4.4 Orthogonal Bases and Gram-Schmidt |
1. Determinant#18: Properties of Determinants#20: Cramer's Rule, Inverse Matrix, and Volume (*) |
5.1 The Properties of Determinants |
2. Eigenvectors#21: Eigenvalues and EigenvectorsHomework 15, hw15.m |
6.1 Introduction to Eigenvalues |
3. Diagonalization#22: Diagonalization and Powers of A |
6.2 Diagonalizing a Matrix |
4. Positive Definite Matrices#25 : Symmetric Matrices and Positive Definiteness#27 : Positive Definite Matrices and Minima |
6.4 Symmetric Matrices 6.5 Positive Definite Matrices |
5. Singular Value Decomposition#29 : Singular Value Decomposition |
6.7 Singular Value Decomposition (SVD) |