Text Book: Stephen H. Friedberg, Arnold J. Insel and Lawrence E. Spence, Linear Algebra, 5th edition, Pearson, 2019. Available on-line for $9.99/month at Pearson.
| Date | Topics covered | Section | Homework problems |
|---|---|---|---|
| 9/7 | Vector spaces | 1.2 | 1.2: #9, 12, 17 |
| 9/12 | Subspaces, Linear Combinations and Systems of Linear Equations | 1.3, 1.4 | 1.3: #8(a), (e), 18, 19, 23 |
| 9/14 | Linear Combinations and Systems of Linear Equations, Linear Dependence and Linear Independence | 1.4, 1.5 |
1.4: #4(a), 5(g), 12,14 1.5: #2(e), 9, 15 |
| 9/19 | Bases and Dimension | 1.6 | 1.6: #3(a), (b), 15, 21, 26 |
| 9/21 | Linear Transformations, Null spaces, and Ranges, The Matrix Representation of a Linear Transformation | 2.1, 2.2 |
2.1: #3, 9(a)-(e), 15, 28
|
| 9/26 | The Matrix Representation of a Linear Transformation, Composition of Linear Transformations and Matrix Multiplication | 2.2, 2.3 | 2.2: #2(a), (g), 4, 8, 10 |
| 9/28 | Composition of Linear Transformations and Matrix Multiplication, Invertibility and Isomorphisms | 2.3, 2.4 | 2.3: #3(a), (b), 4(d) , 12. |
| 10/3 | Invertibility and Isomorphisms, The Change of Coordinate Matrix | 2.4, 2.5 | 2.4: #2(f), 9, 15 |
| 10/5 | The Change of Coordinate Matrix, Dual spaces, | 2.5, 2.6 | 2.5: #3(d), 5, 8 2.6: #2(a), (d), (e), 3, 4 |
| 10/10 | Review | ||
| 10/12 | First Midterm (regular class hour and location; covers 1.2 through 2.6) | ||
| 10/17 | Elementary Matrix Operations and Elementary Matrices, The Rank of a Matrix and Matrix Inverses | 3.1, 3.2 |
3.1: #6,12 3.2: #5(d), (h), 17 |
| 10/19 | Systems of Linear Equations—Theoretical Aspects, Systems of Linear Equations—Computational Aspects | 3.3, 3.4 |
3.3: #8, 10 3.4: #8, 14 |
| 10/24 | Determinants of Order 2, Determinants of Order n | 4.1, 4.2 |
4.1: #9, 11 4.2: #20, 23, 24 |
| 10/26 | Properties of Determinants, Summary — Important Facts about Determinants | 4.3, 4.4 | 4.3: #10, 12, 24 |
| 10/31 | Eigenvalues and Eigenvectors | 5.1 | 5.1: #5(e), 9(a), (b), 20, 21 |
| 11/2 | Diagonalizability | 5.2 | 5.2: #4, 9(a), 13 |
| 11/7 | Invariant Subspaces and the Cayley-Hamilton Theorem | 5.4 | 5.4: #13, 17, 21, 23, 26 |
| 11/9 | The Jordan Canonical Form I | 7.1 | 7.1: #3(b), 9(b), 11 |
| 11/14 | The Jordan Canonical Form II | 7.2 | 7.2: #2, 3, 4(a), 14 |
| 11/16 | Review | ||
| 11/21 | Second Midterm (regular class hour and location; covers 3.3 through 7.2) | ||
| 11/28 | The Minimal Polynomial | 7.3 | 1, 5, 6, 13 |
| 11/30 | Inner Products and Norms, The Gram–Schmidt Orthogonalization Process and Orthogonal Complements | 6.1, 6.2 |
6.1: #4, 8, 9, 11 |
| 12/5 | The Gram–Schmidt Orthogonalization Process and Orthogonal Complements, The Adjoint of a Linear Operator, | 6.2, 6.3 | 6.2: #2(c), 12, 18 |
| 12/7 | Normal and Self-Adjoint Operators, | 6.4 | 6.4: # 2(b), (d), (f) |
| 12/12 | Unitary and Orthogonal Operators and Their Matrices | 6.5 | 6.5: #2 (b), (c), (e), 5(c), 6 |
| 12/14 | Review | ||
| 12/21 | Final exam, 8:00 to 11:00 pm, location to be announced | ||
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