The readings are assigned in: Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley-Cambridge Press, 2009. ISBN: 9780980232714.
Reading assignments are also provided for the newer edition: Strang, Gilbert. Introduction to Linear Algebra. 5th ed. Wellesley-Cambridge Press, 2016. ISBN: 9780980232776.
| SES # | TOPICS | READINGS in 4th Edition | READINGS IN 5TH EDITION |
|---|---|---|---|
| 1 | The geometry of linear equations | 1.1-2.1 | 1.1-2.1 |
| 2 | Elimination with matrices | 2.2-2.3 | 2.2-2.3 |
| 3 | Matrix operations and inverses | 2.4-2.5 |
2.4-2.5 |
| 4 | LU and LDU factorization | 2.6 |
2.6 |
| 5 | Transposes and permutations | 2.7 |
2.7 |
| 6 | Vector spaces and subspaces | 3.1 |
3.1 |
| 7 | The nullspace: Solving Ax = 0 | 3.2 |
3.2 |
| 8 | Rectangular PA = LU and Ax = b | 3.3-3.4 | 3.3 |
| 9 | Row reduced echelon form | 3.3-3.4 | 3.3 |
| 10 | Basis and dimension | 3.5 | 3.4 |
| 11 | The four fundamental subspaces | 3.6 | 3.5 |
| 12 | Exam 1: Chapters 1 to 3.4 | ||
| 13 | Graphs and networks | 8.2 | 3.5, 10.1 |
| 14 | Orthogonality | 4.1 | 4.1 |
| 15 | Projections and subspaces | 4.2 | 4.2 |
| 16 | Least squares approximations | 4.3 | 4.3 |
| 17 | Gram-Schmidt and A = QR | 4.4 | 4.4 |
| 18 | Properties of determinants | 5.1 | 5.1 |
| 19 | Formulas for determinants | 5.2 | 5.2 |
| 20 | Applications of determinants | 5.3 | 5.3 |
| 21 | Eigenvalues and eigenvectors | 6.1 | 6.1 |
| 22 | Diagonalization | 6.2 | 6.2 |
| 23 | Markov matrices | 8.3 | 10.3 |
| 24 | Review for exam 2 | ||
| 25 | Exam 2: Chapters 1-5, 6.1-6.2, 8.2 | ||
| 26 | Differential equations | 6.3 | 6.3 |
| 27 | Symmetric matrices | 6.4 | 6.4 |
| 28 | Positive definite matrices | 6.5 | 6.5 |
| 29 | Matrices in engineering | 8.1 | 10.2 |
| 30 | Similar matrices | 6.6 | 6.2 |
| 31 | Singular value decomposition | 6.7 | 7.1-7.2 |
| 32 | Fourier series, FFT, complex matrices | 8.5, 10.2-10.3 | 10.5, 9.2-9.3 |
| 33 | Linear transformations | 7.1-7.2 | 8.1-8.2 |
| 34 | Choice of basis | 7.3 | 8.3 |
| 35 | Linear programming | 8.4 | 10.4 |
| 36 | Course review | ||
| 37 | Exam 3: Chapters 1-8 (8.1, 2, 3, 5) | ||
| 38 | Numerical linear algebra | 9.1-9.3 | 11.1-11.3 |
| 39 | Computational science | See the Web site for 18.085 | |
| 40 | Final exam |
