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Note that this page will be updated continuously throughout the semester, so make sure to refresh your browser to see the most updated version.
Homework sets will be uploaded here, together with due dates (typically one week after uploading). Quizzes will also be posted once administered, and solutions to both will appear on Sakai .
All sections listed refer to the main textbook Linear Algebra by Friedberg, Insel, and Spence.
| Lecture | Date | Topic | Readings | HW, quizzes, and additional notes |
|---|---|---|---|---|
| Week 1 | ||||
| 1 | Thu 09/06 | Introduction to course, abstract vector space, subspaces | Sections 1.1, 1.2, 1.3 | Homework 1 (due 09/17) |
| Week 2 | ||||
| 2 | Mon 09/10 | Finish subspaces | Section 1.3 | |
| 3 | Thu 09/13 | Linear Combinations | Section 1.5 | |
| Week 3 | ||||
| 4 | Mon 09/17 | Linear independence, introduce basis | Sections 1.5, 1.6 | Homework 2 (due 09/24) |
| 5 | Thu 09/20 | Bases of a vector space, dimension | Section 1.6 | Quiz 1 (Sections 1.1-1.5) |
| Week 4 | ||||
| 6 | Mon 09/24 | Finish basis and dimension, direct sums of subspaces | Section 1.6, Direct Sums reading (not mine) | Homework 3 (due 10/04) |
| 7 | Thu 09/27 | Direct sums, introduction to linear transformations | Section 2.1 | |
| Week 5 | ||||
| 8 | Mon 10/01 | Examples of linear transformations, null space, image | Section 2.1 | Homework 4 (due 10/08) |
| 9 | Thu 10/04 | More properties of range and null space. Dimension (rank-nullity) theorem | Section 2.1 | Quiz 2 (Sections 1.6, 2.1) |
| Week 6 | ||||
| 10 | Mon 10/08 | Coordinates, matrix representations of linear transformations | Sections 2.2, 2.3 | Homework 5 (due 10/18) |
| 11 | Thu 10/11 | Exam 1 | Sections 1.1-1.6, 2.1-2.2 | |
| Week 7 | ||||
| 12 | Mon 10/15 | Matrix representations, linear transformation as matrix-vector multiplication | Sections 2.2, 2.3 | |
| 13 | Thu 10/18 | Composition of linear maps, invertibility | Section 2.3 | Homework 6 (due 10/25) |
| Week 8 | ||||
| 14 | Mon 10/22 | Properties of isomorphisms, change of coordinates | Sections 2.4, 2.5, Chapter 3 | |
| 15 | Thu 10/25 | Change of coordinates, quick review of matrix algebra, determinants | Sections 2.5, Chapter 3, Section 4.1 | Homework 7 (due 11/01) |
| Week 9 | ||||
| 16 | Mon 10/29 | More on determinants | Sections 4.1-4.3 | |
| 17 | Thu 11/01 | Finish determinants, introduce eigenvalues, eigenvectors, diagonalizability | Chapter 4, section 5.1 | Quiz 3 (Sections 2.3-2.5, Chapter 3)
Homework 8 (due 11/08) |
| Week 10 | ||||
| 18 | Mon 11/05 | Continue eigenvalues, eigenvectors, and diagonalizability | Sections 5.1-5.2 | |
| 19 | Thu 11/08 | Continued diagonalizability | Sections 5.1-5.2 | Homework 9 (due 11/29 |
| Week 11 | ||||
| 20 | Mon 11/12 | Finish diagonalizability, more on invariant subspaces | Sections 5.2, 5.4 | |
| 21 | Thu 11/15 | Exam 2 | Sections 2.2-2.5, Chapter 3, Chapter 4, Sections 5.1-5.2 | |
| Week 12 | ||||
| 22 | Mon 11/19 | Cyclic subspaces and their relation to characteristic polynmials | Section 5.4 | I will give Quiz 4 on Thursday 11/29 |
| 23 | Tue 11/20 | Cayley-Hamilton Theorem | Section 5.4 | Homework 9 (due 11/29) |
| Week 13 | ||||
| 24 | Mon 11/26 | Jordan canonical form | Section 7.1 | |
| 25 | Thu 11/29 | Finish Jordan form, minimal polynomial | Section 7.2, 7.3 | Quiz 4 (Sections 5.2 and 5.4)
Homework 10 (due 12/12) |
| Week 14 | ||||
| 26 | Mon 12/03 | Introduction to inner product spaces | Section 6.1 | |
| 27 | Thu 11/29 | Orthogonalization | Section 6.2 | |
| Week 15 | ||||
| 28 | Mon 12/10 | More on orthogonalization, orthogonal complement | Section 6.2 | Quiz 5 (Sections 6.1-6.3) |