Lecture |
Section |
Topics |
1 |
1.2 |
Vector Spaces over
a Field |
2 |
1.3 |
Subspaces |
3 |
1.4,
1.5 |
Linear
Combinations and Systems of Linear Equations; Linear Dependence and Linear
Independence |
4 |
1.5,
1.6 |
Linear
Dependence and Linear Independence; Bases and Dimensions |
5 |
1.6 |
Bases
and Dimensions |
6 |
1.6 |
Bases and Dimensions |
7 |
2.1 |
Linear
Transformations, Null Spaces, and Ranges |
8 |
2.1 |
Linear Transformations,
Null Spaces, and Ranges |
9 |
2.1,
2.2 |
Linear
Transformations, Null Spaces, and Ranges; The Matrix Representation of a
Linear Transformation |
10 |
. |
Midterm
#1 |
11 |
2.2 |
The
Matrix Representation of a Linear Transformation |
12 |
2.3 |
Composition
of Linear Transformations and Matrix Multiplication |
13 |
2.4 |
Invertibility
and Isomorphisms |
14 |
2.4,
2.5 |
Invertibility
and Isomorphisms; The Change of Coordinate Matrix |
15 |
2.5 |
The Change of Coordinate
Matrix |
16 |
4.4 |
Summary - Important
Facts about Determinants |
17 |
5.1 |
Eigenvalues
and Eigenvectors |
18 |
5.1 |
Eigenvalues
and Eigenvectors |
19 |
5.2 |
Diagonalizability |
20 |
5.2 |
Diagonalizability |
21 |
5.2 |
Diagonalizability |
22 |
. |
Midterm
#2 |
23 |
6.1 |
Inner Products and
Norms |
24 |
6.1,
6.2 |
Inner
Products and Norms; The Gram-Schmidt Orthogonalization Process and Orthogonal
Complements |
25 |
6.2 |
The
Gram-Schmidt Orthogonalization Process and Orthogonal Complements |
26 |
6.3 |
The Adjoint
of a Linear Operator |
27 |
6.4 |
Normal
and Self-Adjoint Operators |
28 |
6.4 |
Normal
and Self-Adjoint Operators |
29 |
. |
Catch-up,
Review |
