| Week | Topics | Reading | Homework | |
| 1/24 | Administrivia. Linear Equations: fields, complex numbers, systems of linear equations, matrices, row-reduced echelon form. | 1.1, 1.2, 1.3, 1.4 |
1.2: 1, 3, 5, 7.
1.3: 2, 3, 8.
1.4: 3, 7, 10.
Solutions |
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| 1/31 | Matrix multiplication, invertible matrices.
Fri, Feb 4: last day to add or drop without a W |
1.5, 1.6 |
1.5: 2, 3, 4, 7.
1.6: 2, 8, 9, 10.
2.1: 4, 5, 6.
Solutions |
|
| 2/7 | Vector Spaces: definition, examples, subspaces, bases and dimension. | 2.1, 2.2, 2.3. |
2.2: 1, 2, 4, 7, 8.
2.3: 2, 3, 6, 7, 12.
Solutions |
|
| 2/14 | Coordinates,
row equivalence and computations. |
2.4, 2.5, 2.6. |
2.3: 8. Bonus: 14.
2.4: 1, 2, 4, 7.
2.6: 2, 3, 6.
Solutions |
|
| 2/21 | Linear Transformations: linear transformations, linear transformations as a vector space. | 3.1, 3.2, 3.3 |
3.1: 1, 3, 7, 8, 9.
3.2: 2, 5, 7.
3.3: 2, 4. Bonus: 7.
Solutions |
|
| 2/28 | invertible and nonsingular linear transformations, isomorphisms, representation by matrices. | 3.3, 3.4 |
3.4: 1, 4, 8, 9. Bonus: 12.
Solutions |
|
| 3/7 | change
of basis and
similarity,
linear functionals.
First midterm, on 3/9. Covers thru section 3.4 (more info is here) |
3.4, 3.5 | Extra Credit: rewrite problem 5 of the exam completely. More details
here.
due in class by 3/30 |
|
| 3/14 | Duality, annihilators, and the double dual. | 3.5, 3.6 |
3.5: 2, 3, 4, 8, 9.
3.6: 1.
Solutions |
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| 3/21 |
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| 3/28 | Transpose of a linear transformations,
overview of determinants.
Class cancelled on 3/28. Friday, Apr 1: last day to withdraw or change to P/NC |
3.7, Skim 5.1-5.4 |
3.7: 2, 3, 6, 7.
5.2: 5.
5.4: 3, 4, 5.
Solutions |
|
| 4/4 | Canonical Forms: eigenvalues, eigenvectors, and diagonalization | 6.1, 6.2, 6.3 |
6.2: 1, 4, 5, 8, 9, 13.
Solutions |
|
| 4/11 | Minimal polynomials, invariant subspaces | 6.3, 6.4 |
6.3: 1, 3, 4, 5, 6.
6.4: 3, 4, 7, 9.
Solutions |
|
| 4/18 | diagonalization and the Cayley-Hamilton Theorem, Nilpotent matrices and generalized eigenvectors, Jordan form; | 6.4, 7.1, 7.2, 7.3; Down with Determinants | ||
| 4/25 | no class on 4/25 (passover) Recap and Review. second midterm on 4/29 (covers through 6.4; more info is here) |
8.1 |
7.3: 1, 3, 4, 5.
8.1: 2, 3, 5.
8.2: 1, 2, 9.
Solutions |
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| 5/2 | Inner Product Spaces: inner products, inner product spaces, orthogonality, Gram-Schmidt | 8.1, 8.2, 8.3; Axler's Chapter 6. | ||
| 5/9 | orthogonal complements, minimization.
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