| 1 | The geometry of linear equations | |
| 2 | Elimination with matrices | |
| 3 | Matrix operations and inverses | |
| 4 |
LU and LDU factorization | |
| 5 | Transposes and permutations | Problem set 1 due |
| 6 | Vector spaces and subspaces | |
| 7 | The nullspace: Solving Ax = 0 | |
| 8 | Rectangular PA = LU and Ax = b | Problem set 2 due |
| 9 | Row reduced echelon form | |
| 10 | Basis and dimension | |
| 11 | The four fundamental subspaces | Problem set 3 due |
| 12 | Exam 1: Chapters 1 to 3.4 | |
| 13 | Graphs and networks | |
| 14 | Orthogonality | Problem set 4 due |
| 15 | Projections and subspaces | |
| 16 | Least squares approximations | |
| 17 | Gram-Schmidt and A = QR
| Problem set 5 due |
| 18 | Properties of determinants | |
| 19 | Formulas for determinants | |
| 20 | Applications of determinants | Problem set 6 due |
| 21 | Eigenvalues and eigenvectors | |
| 22 | Diagonalization | |
| 23 | Markov matrices | Problem set 7 due |
| 24 | Review for exam 2 | |
| 25 | Exam 2: Chapters 1-5, 6.1-6.2, 8.2 | |
| 26 | Differential equations | |
| 27 | Symmetric matrices | |
| 28 | Positive definite matrices | |
| 29 | Matrices in engineering | Problem set 8 due |
| 30 | Similar matrices | |
| 31 | Singular value decomposition | Problem set 9 due |
| 32 | Fourier series, FFT, complex matrices | |
| 33 | Linear transformations | |
| 34 | Choice of basis | Problem set 10 due |
| 35 | Linear programming | |
| 36 | Course review | |
| 37 | Exam 3: Chapters 1-8 (8.1, 2, 3, 5) | |
| 38 | Numerical linear algebra | |
| 39 | Computational science | |
| 40 | Final exam | |
