Lecture  Date  Topics covered  Remarks 

Week 1  
1  Mon March 27  Introduction (Section 1.1)  
2  Wed March 29  Vector spaces (Section 1.2)  
3  Fri March 31  Subspaces (Section 1.3)  
Week 2  
4  Mon April 3  Linear combinations (Section 1.4)  
5  Wed April 5  Systems of equations and linear dependence (Sections 1.41.5)  HW 1 due 
6  Fri April 7  Bases and dimension, Part I (Section 1.6)  
Week 3  
7  Mon April 10  Bases and dimension, Part II (Section 1.6)  
8  Wed April 12  Intro to linear transformations (Section 2.1)  HW 2 due 
9  Fri April 14  More on linear transformations and quotient spaces (Section 2.1)  
Week 4  
10  Mon April 17  Matrix representations and composition (Section 2.2)  
11  Wed April 19  Composing linear transformations and matrix multiplication, and visualizing linear transformations (Section 2.3) 
HW 3 due 
12  Fri April 21  Isomorphisms and inverses (Section 2.4)  
Week 5  
13  Mon April 24  Midterm review  
14  Wed April 26  Midterm  
15  Fri April 28  Change of coordinates (Section 2.5)  
Week 6  
16  Mon May 1  First glance at determinants (Sections 4.14.4)  
17  Wed May 3  The determinant as a multilinear function (Sections 4.14.4)  HW 4 due 
18  Fri May 5  Elementary matrices (Section 3.1) and properties of the determinant (Sections 4.1.4.4) 

Week 7  
19  Mon May 8  Even more about determinants (Sections 4.14.4)  
20  Wed May 10  Eigenvectors, eigenvalues and diagonalizable matrices (Section 5.1)  HW 5 due 
21  Fri May 12  More on eigenvectors, eigenvalues and diagonalizable matrices (Section 5.15.2) 

Week 8  
22  Mon May 15  Characteristic polynomials and diagonalizable matrices (Section 5.2)  
23  Wed May 17  First glance at inner product spaces (Section 6.1)  HW 6 due 
24  Fri May 19  More on inner product spaces (Sections 6.16.2)  
Week 9  
25  Mon May 22  GramSchmidt Orthogonalizaton Process (Section 6.2)  
26  Wed May 24  Orthogonal complements and adjoints (Sections 6.26.3)  
27  Fri May 26  Normal linear transformations (Section 6.4)  HW 7 due 
Week 10  
Mon May 29  No class! Memorial day  
28  Wed May 31  Spectral theorems and singular value decomposition
(Sections 6.4, 6.6, 6.7) An application to image compression (see these notes by Paul Dostert) 

29  Fri June 2  Review  
Final  
Wed June 7  Final examination, 8:30  10:20 am 