This repository contains notes and assignments related to the MITOPENCOURSEWARE - Linear Algebra
- Instructor: Prof. Gilbert Strang
- MIT Course Number - 18.06
- Course Link: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.html
Course Description: A basic subject on matrix theory and linear algebra.
| #Session | Topic |
|---|---|
| 1 | The geometry of linear equations |
| 2 | Elimination with matrices |
| 3 | Matrix operations and inverses |
| 4 | LU and LDU factorization |
| 5 | Transposes and permutations |
| 6 | Vector spaces and subspaces |
| 7 | The nullspace: Solving Ax = 0 |
| 8 | Rectangular PA = LU and Ax = b |
| 9 | Row reduced echelon form |
| 10 | Basis and dimension |
| 11 | The four fundamental subspaces |
| 12 | Exam 1: Chapters 1 to 3.4 |
| 13 | Graphs and networks |
| 14 | Orthogonality |
| 15 | Projections and subspaces |
| 16 | Least squares approximations |
| 17 | Gram-Schmidt and A = QR |
| 18 | Properties of determinants |
| 19 | Formulas for determinants |
| 20 | Applications of determinants |
| 21 | Eigenvalues and eigenvectors |
| 22 | Diagonalization |
| 23 | Markov matrices |
| 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 |
| 30 | Similar matrices |
| 31 | Singular value decomposition |
| 32 | Fourier series, FFT, complex matrices |
| 33 | Linear transformations |
| 34 | Choice of basis |
| 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 |