Linear Algebra (Spring 2018) by James Cook at Liberty University

source: James Cook      2018年1月22日
I intent to post my lectures from the Spring 2018 offering of Math 321 at Liberty University. I'll also post the help session which I run most Thursdays. This course has a prerequisite of a proof course, so, it is at a higher level than some linear algebra courses which are intended for a less advanced audience. The basic plan is to cover matrices and equations in Part I, then vectors spaces and basic theory in Part II then in the last third of the course we study Jordan form and the real spectral theorem as well as a few applications.

1 45:36 rings and things, matrices and components, 1-22-18
2 52:42 standard bases and matrix multiplication, 1-24-18
3 59:51 help session on matrix multiplication and index calculation, 1-25-18, part 1
4 12:57 help session on matrix multiplication and index calculation, 1-25-18, part 2
5 41:18 further matrix multiplication, 1-26-18
6 53:11 properties of inverse, types of matrices, 1-29-18
7 51:42 blocks, row operations introduced, 1-31-18
8 59:51 help session on row reduction, 2-1-18, part 1
9 17:22 help session on row reduction, 2-1-18, part 2
10 51:44 from row reduction to elementary matrices, 2-2-18
11 50:55 equivalent conditions for invertibility, 2-5-18
12 59:51 help session on CCP, LI and span, 2-8-18, part 1
13 18:08 help session on CCP, LI and span, 2-8-18, part 2
14 53:46 proof of CCP, super-augmented matrix, 2-9-18
15 49:30 determinants motivated, formulas, expansion by minors, 2-12-18
16 52:34 inverse criteria, Cramer's Rule, inverse formula, 2-14-18
17 59:51 help session, wedges, determinant, evectors, fun, 2-15-18 part 1
18 8:52 help session, wedges, determinant, evectors, fun, 2-15-18 part 2
19 43:00 review for Test 1, 2-16-18
20 50:34 vector spaces and subspaces, 2-21-18
21 59:51 help session, post-mortem of Test 1, subspace examples, 2-22-18, part 1
22 5:11 help session, post-mortem of Test 1, subspace examples, 2-22-18, part 2
23 50:01 span and LI in vector space, 2-23-18
24 49:11 basis and coordinates introduced, 2-26-18
25 52:11 on coordinate calculation, constructive proof of dim, 2-28-18
26 59:51 help session on coordinates and basis calculation, 3-1-18, part 1
27 12:21 help session on coordinates and basis calculation, 3-1-18, part 2
28 49:07 dimension theorems, linear transformation, 3-2-18
29 52:06 linear transformations leading to isomorphism, 3-5-18
30 6:25 examples of transformations on plane etc. 3-7-18, part 1
31 11:11 FToLA and the standard matrix, 3-7-18, part 2
32 9:56 restriction and linear extension, 3-7-18, part 3
33 21:16 matrix of abstract linear map, 3-7-18, part 4
34 59:51 help session on inverse image idea, 3-8-18, part 1
35 9:01 help session on matrix of linear map etc, 3-8-18, part 2
36 53:18 help for the weary, 3-9-18
37 6:22 coordinate change vectors, 3-12-18, part 1
38 7:02 coordinate change vectors, 3-12-18, part 2
39 6:22 coordinate change vectors, 3-12-18, part 3
40 11:19 coordinate change matrices, 3-12-18, part 4
41 11:56 coordinate change matrices, 3-12-18, part 5
42 3:47 rank nullity theorem, linear algebraic proof, 3-12-18, part 6