Week  Topics  Reading  Homework  
1/24  Administrivia. Linear Equations: fields, complex numbers, systems of linear equations, matrices, rowreduced 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 

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 

3/21 


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 5.15.4 
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 CayleyHamilton 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 

5/2  Inner Product Spaces: inner products, inner product spaces, orthogonality, GramSchmidt  8.1, 8.2, 8.3; Axler's Chapter 6.  
5/9  orthogonal complements, minimization.


