Math 417: Matrix Algebra
Syllabus
The syllabus can be found here.
Schedule
| Date | Topics | Book Sections | Homework | Notes and Recording | Additional Notes |
|---|---|---|---|---|---|
| 2022-01-05 Wed | Linear Systems, Gauss Elimination and Matrices | 1.1 and 1.2 | Notes & Recording | ||
| 2022-01-07 Fri | Row operations and Echelon form | 1.2 | 1.1: 14, 20, 30; 1.2: 10, 44, 45 (use calculator for 45) | Notes & Recording | Homework problems due on Canvas |
| 2022-01-10 Mon | Matrix operations, linear combinations | 1.3 | 1.3: 4, 48ab, 58 | Notes & Recording | Homework problems due on Canvas |
| 2022-01-12 Wed | Matrix products | 2.3 | 2.3: 2, 4, 8 | Notes & Recording | Homework problems due on Canvas |
| 2022-01-14 Fri | Linear transformations | 2.1 | 2.1: 8, 12, 26, 28 (look at 2.1 Example 5 for 26, 28) | Notes & Recording | Homework problems due on Canvas |
| 2022-01-17 Mon | No class: MLK Day | ||||
| 2022-01-19 Wed | Injectivity, surjectivity, and invertibility | Notes | Recording did not work for this lecture | ||
| 2022-01-21 Fri | Inverting matrices | 2.4 | 2.4: 2,6,34, 40, 42 | Notes & Recording | Canvas Reflection due today at 11:59pm; Quiz on ; Homework problems due [2022-02-04 Fr |
| 2022-01-24 Mon | Linear maps in geometry | 2.2 | Notes & Recording | Quiz on ; We will continue 2.2 on | |
| 2022-01-26 Wed | Linear maps in geometry continued | 2.2 | 2.2: 20, 32; 2.3: 30 | Notes & Recording | Quiz on ; Homework problems due . |
| 2022-01-28 Fri | Span and image of a linear transformation | 3.1 | 3.1: 6, 24, 32, 34, 37, 38 | Notes & Recording | Quiz in last 15 minutes of class; Homework problems due . |
| 2022-01-31 Mon | Subspaces, Kernel, and Bases | 3.2 | 3.2: 26, 34 | Notes & Recording | Homework problems due |
| 2022-02-02 Wed | Computing bases | 3.3 | 3.3: 30, 38 | Notes & Recording | Homework problems due ; Problem 3.3: 90 is also a cool problem. |
| 2022-02-04 Fri | Rank-Nullity theorem, coordinates | 3.3 | Notes & Recording | Post questions to Piazza that you want to review on | |
| 2022-02-07 Mon | Review for Midterm 1 | Notes & Recording | |||
| 2022-02-09 Wed | Midterm 1 (1.1--3.3) | ||||
| 2022-02-11 Fri | Coordinates, similar matrices | 3.4 | 3.4: 2, 4, 20, 26, 44 | Notes & Recording | Homework problems due . |
| 2022-02-14 Mon | Linear spaces | 4.1 | 4.1: 47, 48 | Notes & Recording | Homework problems due |
| 2022-02-16 Wed | Linear transformations of linear spaces | 4.2 | 4.2: 10, 14, 22, 54 | Notes & Recording | Homework problems due ; Quiz on 3.4, 4.1, 4.2 |
| 2022-02-18 Fri | Matrix of a linear transformation between linear spaces | 4.3 | 4.3: 23, 24, 46 | Notes & Recording | Homework problems due ; Quiz on 3.4, 4.1, 4.2 ; Reflection on Canvas due |
| 2022-02-21 Mon | Dot product, orthogonal bases, orthogonal projections | 5.1 | 5.1: 16, 26, 28 | Notes & Recording | Homework due ; Quiz on 3.4, 4.1, 4.2 ; Reflection on Canvas due |
| 2022-02-23 Wed | Gram-Schmidt process | 5.2 | 5.2: 4, 6, 18, 29 | Notes & Recording | Homework due ; Reflection on Canvas due |
| 2022-02-25 Fri | Gram-Schmidt continued, QR factorization, orthogonal transformations | 5.2, 5.3 | 5.3: 2, 6, 8, 10 | Notes & Recording | Homework due . |
| 2022-02-28 Mon | No class: Mid-Winter Recess | ||||
| 2022-03-02 Wed | No class: Mid-Winter Recess | ||||
| 2022-03-04 Fri | No class: Mid-Winter Recess | ||||
| 2022-03-07 Mon | Orthogonal matrices, matrix transpose, and least squares | 5.3, 5.4 | 5.4: 20, 36, 38 | Notes & Recording | Homework problems due |
| 2022-03-09 Wed | Least squares | 5.4 | Notes & Recording | ||
| 2022-03-11 Fri | Determinants | 6.1 | 6.1: 12, 14, 24, 26, 40, 44 | Notes & Recording | Homework problems due |
| 2022-03-14 Mon | Computing determinants | 6.1, 6.2 | 6.2: 2, 12, 14, 38, 42 | Notes & Recording | Homework problems due |
| 2022-03-16 Wed | Cofactor expansion and geometry of determinants | 6.2, 6.3 | 6.3: 2, 18 | Notes & Recording | Homework problems due |
| 2022-03-18 Fri | Cramer's Rule and applications | 6.3 | Notes & Recording | ||
| 2022-03-21 Mon | Diagonalization and eigenvalues | 7.1 | Notes & Recording | ||
| 2022-03-23 Wed | Review for Midterm 2 | ||||
| 2022-03-25 Fri | Midterm 2 | ||||
| 2022-03-28 Mon | Computing eigenvalues | 7.1, 7.2 | 7.1: 4, 6, 12, 16, 18 | Notes & Recording | Homework problems due |
| 2022-03-30 Wed | Computing eigenvectors and eigenspaces | 7.2, 7.3 | 7.2: 8, 12, 18, 38 | Notes & Recording | Homework problems due |
| 2022-04-01 Fri | Eigenvalues and similarity | 7.3 | 7.3: 8, 10, 24 | Notes & Recording | Homework problems due |
| 2022-04-04 Mon | Complex eigenvalues | 7.5 | 7.5: 14, 20 | Notes & Recording | Homework problems due ; Quiz (7.1--7.3) on . |
| 2022-04-06 Wed | Dynamical Systems | 7.1 | 7.1: 68, 70 | Notes & Recording | Homework problems due ; Quiz (7.1--7.3) on . |
| 2022-04-08 Fri | More dynamical systems | 7.4 | 7.4: 3, 34 | Notes & Recording | Homework problems due ; Quiz (7.1--7.3) on . |
| 2022-04-11 Mon | Symmetric Matrices | 8.1 | 8.1: 4, 14, 16 | Notes & Recording | Reflection due . Ch 8 Homework problems not collected. |
| 2022-04-13 Wed | Singular Value Decomposition | 8.3 | 8.3: 4, 6 | Notes & Recording | Reflection due . Ch 8 Homework problems note collected. |
| 2022-04-15 Fri | Singular Value Decomposition and review | 8.3 | Notes & Recording | Reflection due ; See this website for a cool demo of SVD for image compression. | |
| 2022-04-18 | Review | Notes & Recording |
Date published: Wednesday, January 5, 2022