| Lecture number |
Topics |
| 1 | What is linear algebra? |
|
| 2, 3 | Complex numbers |
|
| 4 | Fundamental theorem of algebra (proof optional) |
|
| 5 | Elementary set theory |
|
| 6,7 | Vector spaces and subspaces |
|
| 8 | Direct sum, linear span |
|
| 9 | Linear independence of vectors |
|
| 10,11 | Bases and dimension of vector spaces |
|
| 12 | Linear maps |
|
| 13 | Null space and range of linear maps |
|
| 14 | Dimension formula for a linear map |
|
| 15 | Matrix of a linear map |
|
| 16 | Invertibility |
|
| 17 | Gaussian Elimination, factoring into elementary matices |
|
| 18 | Determinants |
|
| 19 | Properties of the determinant |
|
| 20 | Eigenvalues and Eigenvectors |
|
| 21 | Existence of eigenvalues |
|
| 22 | Inner product spaces |
|
| 23 | Cauchy-Schwarz inequality, triangle inequality |
|
| 24 | Orthonormal bases, Gram-Schmidt process |
|
| 25 | Orthogonal projections, minimization |
|
| 26 | Change of basis |
|
| 27 | Diagonalization |
|
|
MAT 67