There are two big topics in Linear Algebra; one is solving a system of linear equations, and the other is the eigenvalue and eigenvector. We understand these two topics by understanding vector spaces and linear transformations, and hopefully learning the domain and codomain of a linear transformation can be decomposed into the four fundamental spaces. These concepts are summarized as the Singular Value Decomposition Theorem.

More specifically, we will study
* vector space and matrix, linear system
* PA=LU decomposition
* four fundamental spaces
* rotations in 2D and 3D
* orthogonality and projections
* least square method
* determinant
* eigenvalues and eigenvectors, diagonalization
* matrix powers and matrix exponential
* Jordan normal form
* positive definite matrix and congruence
* Singular Value Decomposition

None

Week 01: 1.1, 1.2, 1.3, 1.4
Week 02: 1.5, 1.6
Week 03: 2.1, 2.2
Week 04: 2.3, 2.4
Week 05: 2.6
Week 06: 3.1, 3.2
Week 07: 3.3, 3.4
Week 08: midterm week
Week 09: 4.1, 4.2, 4.3
Week 10: 4.3, 4.4
Week 11: 5.1, 5.2
Week 12: 5.3, 5.4
Week 13: 5.5, 5.6
Week 14: 6.1, 6.2
Week 15: 6.3
Week 16: final week

Lecture and recitation sessions*
(* quiz will be held on each recitation sessions, based on the problem set below)

Problem set:

1.3 / 12,13,21,22,23,25,27,28,32

1.4 / 2,5,6,7,9,16,17,18,19,20,21,27,28,29,35,36,39,40,45,46,47,48,53,58

1.5 / 4,7,9,10,11,12,17,18,19,21,23,25,29,31,32,42,44

1.6 / 1,2,3,4,5,6,7,9,10,11,12,13a,14,16,18,20,21,23,25,28,29,31,32,36,37,38,39,41,49,50,51,52,54,56,57,59,60

2.1 / 2,3,4,5,6b,7,8,10,11,15,16,17,18,19,20,22,24,25,26,27,28,29

2.2 / 2,3,4,5,6,8,12,21,26,27,29,30,34,35,36,40,41,43,45,49,54,56

2.3 / 3,4,7,8,9,15,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,35,36,37,41,45

2.4 / 1,2,3,6,8,9,10,13,15,16,17,23,27

2.6 / 1,2,3,4,5,8,9,11,12,14,18,19,20,21,24,25,26,27,30,31,35,38,42,47,48,50

3.1 / 2,3,5,6,7,8,9,10(typo: R^2->R^3),11,13,14,15,16,17,18,19,20,24,25,26,27,28,31,33,34,35,36,38,39,40,41,44,45,47,51,52

3.2 / 2,5,7,8,9,10,11,12,17b,19,20,22,25

3.3 / 1,4,5,6,9,10,11,12,13,14,15,16,17,18,20,21,22,23,26

3.4 / 1,3,4,6,7,8,9,10,11,12,14,15,16,20,23,28,30,32

4.2 / 2,3,4,5,7,8,9,13,16,18,19,21,23,26,27,28,29

4.3 / 1,3-4,11,13,14,20,24,27,35a,b,42

4.4 / 1,2a,5,7,14,18,20,21,27,29,32,34,35

5.1 / 1,3,4,6,7,8,9,10,15,16,18,19,20,22,23,24,25,27,28,30,31,38

5.2 / 1,3,4,5,6,8,9,10,13,14,15,16,17,20,22,23,24,26,27,36,38,39,40,41,42

5.3 / 1,6,8,9,10,12,20,24,25,27,28

5.4 / 1,2,5,6,7,9,10,11,14,16,19,21,23,25,30,35,36,37,38,39(typo:36->35),40,41,43

5.5 / 4,7,9,15,19,20,22,25,26,30,31,32,33,34,35,39,41,42,43,44,50

5.6 / 1,2,4,8,11,12,16,19,20,23,28,31,32,33,37; Appendix B / 2,4,5,6

6.1 / 2,3,5,8,9,10,11,13,14,15,16,17(pay special attention to whether columns are linearly independent),18,20,21,22

6.2 / 1,2,3,5,6,7,8,9,10,12,13,14,16,19,21,22,23,24,25,26,27,28,30,31,32,34,36

6.3 / 1(A is given in (b)),2,3,6,7,9,10,11,14,15,16,18,19,20,22,23