
Date 
Topic 
Book 
Homework 
Practice Problems 
Jan. 
10 
Introduction to determinants 




12 
Axiomatic characterization of the determinant 




13 
Bilinearity and determinants in ℝ^{2} 




17 
Trilinearity and determinants in ℝ^{3} 
§4.2 



19 
The determinant in any dimension 
§4.2 



20 
Permutations and the determinant formula 
§4.2 
H13 


24 
Calculating the determinant 
§4.2 
A13 
1 – 15


26 
More determinant calculations 
§4.2 

16 – 20, 22, 23, 26 – 29


27 
Cramer's Rule 
§4.2 
H14 
35 – 38, 57 – 60


31 
The classical adjoint 
§4.2 
A14 
61 — 64

Feb. 
2 
Bases and coordinates 
§6.3 

1, 2, 3, 4 (part a only)


3 
Change of basis 
§6.3 
H15 
1, 2, 3, 4 (parts b, c, d, e)

Feb. 
7 
Change of basis II 

A15 


9 
Inclass exam #3 




10 
Iterating linear transformations 
§3.7 
H16 
5 – 8, 10


14 
Eigenvalues and Eigenvectors 
§4.3 
A16 
§4.1: 13–17


16 
Finding Eigenvalues and Eigenvectors 
§4.3 

1–6 (parts a and b)


17 
Diagonalization 
§4.4 
H17 
5–7


21 





23 
Reading Week 




24 





28 
Eigenspaces 
§4.3 
A17 
1–6 (parts c and d)

Mar. 
2 
More Diagonalization 
§4.4 

8–15, 16–18


3 
End of the proof on Diagonalization 
§4.4 
H18 


7 
Complex Numbers 
App. C 
A18 


9 
Complex Eigenvalues and Eigenvectors 




10 
Dominant Eigenvalues 
§4.5 
H19 
9–12


14 
The Gerschgorin disk theorem 
§4.5 
A19 
47–50


16 
Inclass exam #4 




17 
Some Eigenapplications 
§4.6 
H20 
7–9


21 
Introduction to abstract vector spaces 
§6.1 
A20 
5–10


23 
Subspaces, bases, coordinates 
§6.12 

§6.1: 29, 33, 35, 36


24 
Linear transformations 
§6.4 
H21 
5, 7, 8, 16


28 
Dimension, Ranknullity theorem 
§6.5 
A21 
3, 4, 10, 12


30 
Inner product spaces 
§7.1 

1, 2, 5, 9, 10, 11


31 
Orthonormal bases 
§5.1 
H22 
1–6, 11–15

Apr. 
4 
GramSchmidt orthogonalization 
§5.3 
A22 
1–6, 11, 12


6 
Leastsquares solutions 
§7.3 

19, 20, 23, 24


7 
Leastsquares solutions II 
§7.3 
H23 


11 


A23 


13 


H24 


14 


A24 
