Algebra (2015) by Aviv Censor at Technion

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source: Technion    2015年11月23日
Algebra 1M - international
Course no. 104016
Dr. Aviv Censor
Technion - International school of engineering

01 - Introduction 9:13
02 - Sets of numbers 41:58
03 - Fields 32:01
04 - More properties of fields 18:53
05 - Complex numbers 47:34
06 - The Complex conjugate, the modulus and division 51:30
07 - Polar form 27:59
08 - Multiplication, division, powers and roots 39:26
09 - Polynomials 16:40
10 - Roots of polynomials 1:06:26
11 - Matrices 35:01
12 - Operations on matrices 21:49
13 - Matrix multiplication 21:48
14 - Properties of matrix multiplication 33:42
15 - Systems of linear equations 22:20
16 - Solving systems of linear equations 17:01
17 - The method of row-reduction 1:02:06
18 - Determining the number of solutions 47:38
19 - Homogeneous vs. non homogeneous systems 45:31
20 - The space R^n 29:12
21 - Vector spaces 46:18
22 - Vector subspaces 30:24
23 - More examples of subspaces 21:23
24 - Intersections and sums of subspaces 27:05
25 - Direct sums of subspaces 29:22
26 - Linear combinations and spans 35:20
27 - Determining if v belongs to a span 18:54
28 - Linear independence 20:14
29 - Determining linear independence 59:07
30 - Theorems about linear independence 39:56
31 - More on spans and linear independence 37:26
32 - Bases of vector spaces 20:18
33 - The dimension of a vector space 21:57
34 - Properties of bases 17:44
35 - Properties of bases (continued) 1:01:48
36 - Bases and dimensions of subspaces 52:16
37 - Coordinate vectors 34:15
38 - The dimension of Row(A) and Col(A) 44:47
39 - The rank-nullity theorem 32:41
40 - Invertible matrices 20:57
41 - Determining invertibility and finding the inverse 1:01:07
42 - Determinants 34:21
43 - Properties of determinants 31:33
44 - Invertibility and the determinant 21:08
45 - The matrix adj(A) 30:43
46 - Cramer's rule 13:12
47 - Which method is better? 7:02
48 - Linear maps 37:19
49 - Ker(T) and Im(T) 34:28
50 - Some geometric examples 26:48
51 - Properties of Ker(T) and Im(T) 40:07
52 - The rank of T 25:18
53 - The rank-nullity theorem revisited 37:12
54 - Matrix representation of linear maps 42:07
55 - Matrix representation of linear maps (continued) 1:00:27
56 - Operations on linear maps 58:21
57 - Compatability with operations on matrix representations 32:28
58 - Isomorphism 41:42
59 - Hom(V,W) 44:11
60 - Similarity of matrices 1:10:35
61 - Properties of similar matrices 22:29
62 - Diagonalization 25:32
63 - Diagonalization - a simple example 47:20
64 - Finding eigenvalues and eigenvectors 1:11:38
65 - An example 34:59
66 - Multiplicities of eigenvalues 33:11
67 - More on eigenvalues 1:13:41
68 - Powers of diagonalizable matrices 10:51
69 - The Cayley-Hamilton theorem 10:35
70 - Inner product 1:05:08
71 - Norm 30:24
72 - Inner product and norm give geometry 53:46
73 - Orthogonality 57:14