Welcome

Syllabus

Homework

Schedule

All linked section numbers direct to pdf copies of the lecture notes I used. Resources used in class will appear in the supplements column.

Week	Sec.	Topic	Supplements
1	1.1	Systems of linear equations
	1.2	Row reduction and echelon forms	Handouts: Part 1
2	1.2	- -	Part 2 (written) Summary
	1.3	Vector equations	Visualizing vectors: In R3 (with components) Addition (with commutativity) Linear combinations example
3	1.3	- -
	1.4	The matrix equation Ax = b
	1.5	Solution sets of linear systems	Graphical examples of solution sets.
4	1.5	- -
	1.7	Linear independence
	1.8	Introduction to linear transformations	Some nice videos on linear transformations Two dimensions Three dimensions Differing dimensions
5	1.8	- -
	1.9	The matrix of a linear transformation	Standard matrices for common transformations
	2.1	Matrix operations	Basic properties of matrix algebra A neat connection.
6	2.1	- -
	2.2	The inverse of a matrix	Computing the inverse of a 'large' matrix (.mw)
	2.3	Characterizations of invertible matrices	The invertible matrix theorem
	2.5	Matrix factorizations
7	2.5	- -
	Exam I	Chapters 1 and 2.	"Study guide"
8	3.1	Determinants
	3.2	Properties of the determinant
	3.3	The geometry of the determinant	Volume under a linear transformataion Visualizing area under a linear transformation A nice discussionn of the geometry of the determinant
9		Spring recess
10	3.3	- -
	4.1	Vector spaces	The axioms of a vector space A family of examples of vector spaces and subspaces
11	4.1	- -
	4.2	Null space and column space	Contrasting the null and column space of a matrix
	4.3	Linearly independent sets; bases
12	4.3	- -
	4.4	Coordinate systems	A natural subspace with no natural coordinates
13	Exam II	Chapters 3 and 4.	"Study guide"
	5.1	Eigenvectors and eigenvalues	A two dimensional eigenspace
	5.2	The characteristic equation
14	5.2	- -
	5.3	Diagonalization
	5.4	Eigenvectors and linear transformations
15	5.4	- -
	6	Norms, orthogonality and inner products
16	Final	Cumulative.	"Study guide"