Most of the reading assignments below refer to the textbook:
[Axler] = Axler, Sheldon J. Linear Algebra Done Right. Springer, 2004. ISBN: 9780387982588. [Preview with Google Books]
A few topics not fully covered in the textbook are discussed in supplementary notes available in the Study Materials section. These include:
[F] = Notes on Finite Fields
[OSI] = Notes on One-sided Inverses
[GE] = Notes on Gaussian Elimination
[OB] = Notes on Orthogonal Bases
[ST] = Proof of the Spectral Theorem
[EIG] = Notes on Generalized Eigenvalues
| LEC # | TOPICS | READINGS |
|---|---|---|
| 1 | Definition of vector spaces, properties | [Axler] Chapter 1, pp. 2–12. |
| 2 | Subspaces, sums and direct sums | [Axler] Chapter 1, pp. 13–18. |
| 3 | Span, independence, bases | [Axler] Chapter 2, pp. 21–31. |
| 4 | Bases and dimension | [Axler] Chapter 2, pp. 31–34. |
| 5 | Linear maps, null space / range | [Axler] Chapter 3, pp. 38–47. |
| 6 | Matrices, invertibility | [Axler] Chapter 3, pp. 48–58. |
| 7 | Exam 1 on Chapters 1–3 | No Readings |
| 8 | Finite fields. Systems of equations. | [F], [GE], [OSI] |
| 9 | Gaussian elimination | [GE] |
| 10 | Counting over Fp. Invariant subspaces. | [Axler] Chapter 5, pp. 75–79, [F] |
| 11 | Finding eigenvectors | [Axler] Chapter 5, pp. 80–81. |
| 12 | Upper triangular and diagonal matrices | [Axler] Chapter 5, pp. 81–90. |
| 13 | Eigenvectors over R and Fp | [Axler] Chapter 5, pp. 91–93, [F] |
| 14 | Exam 2 on Chapters 1–5 | No Readings |
| 15 | Inner products, Gram-Schmidt | [Axler] Chapter 6, pp. 97–111, [OB] |
| 16 | Orthogonal projection, minimization | [Axler] Chapter 6, pp. 111–16. |
| 17 | Adjoint, self-adjoint, normal | [Axler] Chapter 7, pp. 127–32. |
| 18 | Spectral theorem | [Axler] Chapter 7, pp. 132–44, [ST] |
| 19 | Positive operators | [Axler] Chapter 7, pp. 144–47. |
| 20 | Isometries, polar decomposition | [Axler] Chapter 7, pp. 147–57. |
| 21 | Exam 3 on Chapters 1–7 | No Readings |
| 22 | Generalized eigenspaces | [Axler] Chapter 8, pp. 163–68, [EIG] |
| 23 | Generalized eigenspace decomposition | [Axler] Chapter 8, pp. 173–78, [EIG] |
| 24 | Characteristic polynomial | [Axler] Chapter 8, pp. 168–73. |
| 25 | Determinant | [Axler] Chapter 10. |
| 26 | Trace, canonical commutation relations | [Axler] Chapter 10. |
