| Date | Reading | Topics | Graded Problems | Recommended Problems |
|---|---|---|---|---|
| 9/07 | 1.3, 1.4 | Gaussian Elimination; Review of Matrix Algebra | ||
| 9/12 | 1.4 | Review of Matrix Algebra | 10, 24 | 11, 13, 14, 15, 17, 20, 22, 23, 25, 31, 39, 42, 46, 49, 51, 52 |
| 1.5 | Gaussian Elimination by Elementary Matrices; LU and LDU Factorizations; | 12, 24 | 4, 5, 6, 7, 9, 11, 13, 15, 19, 23, 25, 33 | |
| 1.6 | Matrix Inverses | 12 | 3, 5, 9, 11, 17, 19, 21, 25, 29, 35, 40, 45, 54, 56 | |
| 9/14 | 2.1 | Vector Spaces and Subspaces | 14 | 2, 5, 6, 8, 9, 18, 19, 25, 29, 30 |
| 2.2 | Solving Linear Systems | 26, 62 | 3, 5, 7, 9, 12, 13, 15, 20, 21, 25, 35, 39, 41, 42, 44, 45, 51, 53, 56, 61, 66, 68 | |
| 9/19 | 2.3 | Linear Independence, Basis, and Dimension; Column Space, Null Space, Uniqueness of rref(A) | 28, 34 | 3, 4, 7, 8, 11, 13, 19, 22, 23, 29, 31, 35, 37 |
| 9/21 | 2.4 | Four Fundamental Subspaces | 10, 18 | 3, 5, 7, 13, 15, 17, 21, 25, 27, 29, 35, 37 |
| 2.6 | Linear Transformations and Their Matrices | 8 | 1, 3, 5, 7, 11, 15, 18, 23, 30, 37 | |
| 9/26 | 3.1 | Orthogonal Spaces | 32 | 5, 7, 9, 11, 12, 15, 19, 21, 25, 27, 30, 33, 39, 49, 51 |
| 3.2 | Inner Products and Projections | 14 | 1, 5, 7, 9, 11, 17, 19, 21, 22, 23 | |
| 9/28 | 3.3 | Projections and Least-squares Approximations | 4, 6, 12, 14, 18 | 1, 3, 7, 9, 11, 15, 19, 25, 27 |
| 10/3 | 3.4 | Orthonormal Bases; Gram-Schmidt Process; QR Factorization | 12, 16, 32 | 2, 3, 4, 5, 6, 9, 11, 13, 15, 17, 19, 27, 31 |
| 10/5 | 4.1 | Determinants | ||
| 4.2 | Properties of the Determinant function | 14, 16 | 1, 3, 4, 5, 7, 8, 9, 15, 19, 21, 27 | |
| MATLAB Assignment # 1 due 10/10 | ||||
| 10/10 | 4.3 | Formulas for Determinants | 28, 34, 36 | 1, 3, 5, 11, 15, 25, 35 |
| 10/12 | 4.4 | Determinant Formulas for Matrix Inverse; Cramer's Rule | 4, 18 | 1, 3, 7, 9, 13, 19, 21, 25 |
| 10/17 | 5.1 | Eigenvalues and Eigenvectors | 10, 14 | 1, 3, 9, 11, 13, 15, 18, 22, 23, 28, 30 |
| 5.2 | Diagonalization | 8, 22, 24 | 1, 2, 3, 4, 5, 7, 11, 12, 13, 14, 23, 29, 35, 40 | |
| MATLAB Assignment # 2 due 10/19 | ||||
| 10/19 | 5.3 | Difference Equations | 16, 18 | 3, 5, 7, 17, 27 |
| 5.4 | Differential Equations | 12 | 1, 5, 7, 9, 13, 19, 21, 23, 27 | |
| 10/24 | Midterm Exam on Chapters 1-4 (closed book) | |||
| 10/26 | 5.4 | Matrix Exponentials | 34, 40 | 33, 35, 37, 39 |
| 5.5 | Complex Vector Spaces; Hermitian Matrices | 8, 12, 18, 46 | 1, 2, 3, 5, 6, 7, 11, 13, 15, 17, 19, 23, 25, 27, 28, 33, 38, 45, 47 | |
| 10/31 | 5.6 | Schur Triangular Form; Unitary Diagonalization of Normal Matrices | 16, 20, 22 | 3, 4, 5, 6, 15, 17, 21, 23 |
| 11/2 | 3.5, Notes | Discrete Fourier Transform; Shift Operator and Circulant Matrices | 7 | 1, 4, 9 |
| MATLAB Assignment # 3 due 11/07 | ||||
| 11/07 | 3.5, Notes | Diagonalization of Circulant Matrices; Fast Fourier Transform | 8, 20 | 11 |
| 11/09 | 5.6 | Cayley-Hamilton Theorem; Canonical forms for matrices | 25, 29 | |
| 11/14 | 5.6 | Jordan Canonical Form--Statement and Examples | 36 | 35 |
| App. B | The Jordan Canonical Form--Statement and Examples | 1 | 5 | |
| 11/16 | App. B | Jordan Canonical Form--Proof; Applications to Differential Equations | 3, 6 | 2, 4, 7 |
| MATLAB Assignment # 4 due 11/21 | ||||
| 11/21 | 6.1 | Quadratic Forms | 2, 18 | 1, 3, 5, 7, 9, 17, 19 |
| 6.2 | Positive-definite Matrices | 20, 28, 32 | 1, 5, 7, 9, 15, 17, 19, 23, 27 | |
| NO CLASS November 23 | ||||
| 11/28 | 6.2 | Indefinite Quadratic Forms; Law of Inertia | 32 | |
| 11/30 | 6.3 | Singular Value Decomposition | 2 | 1, 3, 5, 7, 15, 19 |
| 12/05 | 6.4 | Minimum Principles; Rayleigh Quotient | 1, 3, 5, 6, 7, 8, 9, 16 | |
| 12/07 | 7.2-3 | Matrix Norm and Condition Number | 3, 5, 7, 8, 11, 13, 14 | |
| 7.3 | Power Method | |||
| MATLAB Assignment # 5 due 12/12 | ||||
| 12/12 | 7.3 | Hessenberg form and QR algorithm | ||
| 12/14 | 7.3 | QR algorithm and Inverse Power Method
for Eigenvectors |
3, 5, 6, 7 | |
| 12/23 | Final Exam (closed book) |