Linear Algebra

Calendar

LEC #	TOPICS	KEY DATES
1	Definition of vector spaces, properties
2	Subspaces, sums and direct sums
3	Span, independence, bases
4	Bases and dimension	Problem set 1 due
5	Linear maps, null space / range
6	matrices, invertibility	Problem set 2 due
7	Exam 1 on Chapters 1–3
8	Finite fields. Systems of equations.
9	Gaussian elimination
10	Counting over Fp. Invariant subspaces.	Problem set 3 due
11	Finding eigenvectors
12	Upper triangular and diagonal matrices	Problem set 4 due
13	Eigen vectors over R and Fp	Problem set 5 due
14	Exam 2 on Chapters 1–5
15	Inner products, Gram-Schmidt
16	Orthogonal projection, minimization
17	Adjoint, self-adjoint, normal	Problem set 6 due
18	Spectral theorem
19	Positive operators	Problem set 7 due
20	Isometries, polar decomposition
21	Exam 3 on Chapters 1–7
22	Generalized eigenspaces
23	Generalized eigenspace decomposition	Problem set 8 due
24	Characteristic polynomial	Problem set 9 due
25	Determinant
26	Trace, canonical commutation relations
	Final Exam