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Introduction
Algebra 1M
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הטכניון - מכון טכנולוגי לישראל
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Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
Course content
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44h 7m left
Introduction
9:13
2
Sets of numbers
41:58
3
Fields
32:01
4
More properties of fields
18:53
5
Complex numbers
47:34
6
The Complex conjugate, the modulus and division
51:30
7
Polar form
27:59
8
Multiplication, division, powers and roots
39:26
9
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
