This is a tentative schedule for what I have covered and what I plan to cover in class each day. This section will be updated regularly during the semester.
| Date |
Topic |
Homework |
Due |
| Mon, August 26 | Introduction. Fields. | Part of homework 1 | Sep 4 |
| Wed, August 28 | Vector spaces. Subspaces. | Chapter 1, Ex. 3,5ac,6,9,13,15 | Sep 4 |
| Fri, August 30 | Sums of subspaces. Direct sums. Spans | ||
| Mon, September 2 | Labor day; No classes | ||
| Wed, September 4 | Linear independence. | Chapter 2:3,4,6,8,9,11,12,14 | Sep 11 |
| Fri, September 6 | Basis and dimension. | ||
| Mon, September 9 | Linear maps | ||
| Wed, September 11 | Linear maps | Chapter 2:16,17 | Sep 18 |
| Fri, September 13 | The matrix of a linear map | Chapter 3:2,4,6,7,9,13 | Sep 18 |
| Mon, September 16 | Products and invertibility | Chapter 3:16,21 | Sep 25 |
| Wed, September 18 | Isomorphism | Chapter 3:22,23,25 | Sep 25 |
| Fri, September 20 | Polynomials | Chapter 4:2,4,5 | Sep 25 |
| Mon, September 23 | Invariant subspaces. Existence of an eigenvalue. | Chapter 5:1,3,4,8 | Oct 4 |
| Wed, September 25 | Upper-triangularizable operators | ||
| Fri, September 27 | Diagonalizable operators. Invariant subspaces of real vector spaces. Projections. | Chapter 5:11,15,17,20 | Oct 9 |
| Mon, September 30 | Midterm 1 | ||
| Wed, October 2 | Inner product spaces | Chapter 6:3,5,6,9 | Oct 9 |
| Fri, October 4 | Cauchy-Schwarz inequality. Orthonormality. | Chapter 6:10,13,18,20 | Oct 16 |
| Mon, October 7 | Gram-Schmidt process; Orthogonal projections | Chapter 6:24,26,31,32 | Oct 16 |
| Wed, October 9 | Linear functionals and the adjoint of a linear transformation | ||
| Fri, October 11 | Normal and self-adjoint operators | ||
| Mon, October 14 | The Complex Spectral Theorem | Chapter 7:1,3,7,9 | Oct 23 |
| Wed, October 16 | The Real Spectral Theorem | Chapter 7:10,12,14,15 | Oct 23 |
| Fri, October 18 | Mid-Semester Break; No Classes | ||
| Mon, October 21 | Positivity. | Chapter 7:16,17,19,20 | Oct 30 |
| Wed, October 23 | Isometries. | Chapter 7:21,22,24 | Oct 30 |
| Fri, October 25 | Polar decomposition. | ||
| Mon, October 28 | Singular-value decomposition. | Chapter 7:31,34 | Nov 13 |
| Wed, October 30 | Characteristic polynomials. | Chapter 8:1,5,8,10 | Nov 13 |
| Fri, November 1 | Cayley-Hamilton Theorem | ||
| Mon, November 4 | Midterm 2 | ||
| Wed, November 6 | Square roots | Chapter 8:12,16 | Nov 13 |
| Fri, November 8 | The minimal polynomial | Chapter 8:17,18,20,22,23,28 | Nov 22 |
| Mon, November 11 | Jordan form | Chapter 9:1,3,4,7 | Nov 22 |
| Wed, November 13 | Block diagonal matrices for operators on real vector spaces | ||
| Fri, November 15 | Characteristic polynomials of operators on real vector spaces | ||
| Mon, November 18 | Structure of operators on real vector spaces | Chapter 9:8,10,11,13 | Dec 4 |
| Wed, November 20 | Change of bases | ||
| Fri, November 22 | Trace and determinant of an operator | Chapter 10:3,6,8,15,17,22 | Dec 4 |
| Mon, November 25 | Equality of the determinants of an operator and its matrices | ||
| Wed, November 27 | Thanksgiving Holiday; No Classes | ||
| Fri, November 29 | Thanksgiving Holiday; No Classes | ||
| Mon, December 2 | Bilinear forms | ||
| Wed, December 4 | Tensor products | ||
| Fri, December 6 | Tensor products |