Week of	Tuesday	Thursday	Topics
8/25	1.1	1.2, 1.3	Sets and functions, Vector Spaces, subspaces.
9/1	1.4, 1.5	1.5, 1.6	Linear combinations, linear dependence, basis, dimension.
9/8	1.6	2.1	Dimension. Linear transformations, nullspace, range.
9/15	2.2, 2.3	2.3, 2.4	Matrices, composition and multiplication, invertibility and isomorphisms.
9/22	2.5, 2.6	3.1, 3.2	Coordinate change, dual spaces. Elementary operations, ranks and inverses of matrices.
9/29	3.3, 3.4	Midterm	Systems of linear equations. Midterm on chapters 1 and 2.
10/06	3.4	4.1, 4.2	More on systems. Determinants.
10/13	4.3--4.5	5.1	Properties of determinants. Eigenvector and eigenvalues
10/20	5.2	5.4	Diagonalizability. Invariant subspaces.
10/27	5.4	6.1	Cayle-Hamilton theorem. Inner products and norms.
11/03	6.2	Midterm	Orthogonal Projections and Gram-Schmidt. Midterm on chapter 3, 4 and 5..
11/10	Holiday	6.3, 6.4	Adjoints and normality.
11/17	6.4, 6.5	7.1	Unitary and orthogonal operators. Jordan canonical form.
11/24	7.1, 7.3	Holiday	More on the Jordan canonical form. Minimal polynomial.
12/02	7.3	7.4	Minimal polynomial, rational canonical form.

The above schedule is just a rough guide and subject to change as the course progresses.