| Day | Topics | Reading |
|---|---|---|
| Tu. 1/20 | Introduction to the course. Review of linear algebra from Math 254. |
. |
| Th. 1/22 | Vector spaces and subspaces. | [Ax] Secs. 1A-C |
| Tu. 1/27 | Fields and the complex numbers. Sums of subspaces. |
[Ax] Secs. 1A, 1C |
| Th. 1/29 | Linear independence. Basis for a vector space, dimension. |
[Ax] Sec. 2A-B |
| Tu. 2/3 | Bases, dimension, and direct sums. | [Ax] Sec. 2B-C |
| Th. 2/5 | Linear maps as a vector space. Null space and range. |
[Ax] Sec. 3A-B |
| Tu. 2/10 | The fundamental theorem on linear maps. Proving fundamentals: Problems solving session. |
[Ax] Sec. 3A-B |
| Th. 2/12 | .Coordinates (with respect to a basis). Matrices for linear maps (with respect to two bases). |
[Ax] Sec. 3C-D |
| Tu. 2/17 | Factoring a matrix (or linear map. Invertibility and isomorphism. Problem solving session. |
[Ax] Sec. 3CD |
| Th. 2/19 | Products and quotient spaces. | [Ax] Sec. 3E |
| Tu. 2/24 | Polynomials. | [Ax] Sec. 4 |
| Th. 2/26 | Operators and invariant subspaces.
Eigenvalues and eignevectors. |
[Ax] Sec. 5.A |
| Tu. 3/3 | The minimal polynomial of an operator. | [Ax] Sec. 5.B |
| Th. 3/5 | Test 1. | [Ax] Sec. 1ABC, 2ABC, 3ABCDE |
| Tu. 3/10 | The minimal polynomial and upper triangular matrices. | [Ax] Sec. 5BC |
| Th. 3/12 | .Operators that are upper triangularizable. | [Ax] Sec. 5C |
| Tu. 3/17 | Operators that are diagonalizable. | [Ax] Sec. 5D |
| Th. 3/19 | Generalized eigenspaces decompose a coplex vector space. |
[Ax] Sec. 8AB |
| Tu. 3/24 | Nilpotent matrices and Jordan from. | [Ax] Sec. 8ABC |
| Th. 3/26 | Inner products and norms. | [Ax] Sec. 6A |
| Tu. 4/7 | Test 2 | [Ax] Ch 5A-D, 8A-C (parts of). |
| Th. 4/9 | . | [Ax] Sec. |
| Tu. 4/14 | . | [Ax] Sec. |
| Th. 4/16 | . | [Ax] Sec. |
| Tu. 4/21 | . | [Ax] Sec. |
| Th. 4/23 | . | [Ax] Sec. |
| Tu. 4/28 | . | [Ax] Sec. |
| Th. 4/30 | . | [Ax] Sec. |
| Tu. 5/5 | . | [Ax] Sec. |
| Tu. 5/122 | Final Test. | [Ax] Mainly Ch 6,7. Also Ch 1-3, 5,8 |