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