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Uedu Open / Linear Algebra
18.06SC

Linear Algebra

Prof. Gilbert Strang | Fall 2011
Science & Math Mathematics Linear Algebra
前往原始課程
CC BY-NC-SA 4.0
課程簡介

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

  • A complete set of Lecture Videos by Professor Gilbert Strang.
  • Summary Notes for all videos along with suggested readings in Prof. Strang’s textbook Linear Algebra.
  • Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
  • Problem Sets to do on your own with Solutions to check your answers against when you’re done.
  • A selection of Java® Demonstrations to illustrate key concepts.
  • A full set of Exams with Solutions, including review material to help you prepare.
課程資訊
來源MIT 開放式課程
科系Mathematics
語言English
影片數74
課程影片 (74)
1
An Interview with Gilbert Strang on Teaching Linear Algebra
An Interview with Gilbert Strang on Teaching Linear Algebra
2
Course Introduction | MIT 18.06SC Linear Algebra
Course Introduction | MIT 18.06SC Linear Algebra
3
1. The Geometry of Linear Equations
1. The Geometry of Linear Equations
4
Geometry of Linear Algebra
Geometry of Linear Algebra
5
Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008
6
An Overview of Key Ideas
An Overview of Key Ideas
7
2. Elimination with Matrices.
2. Elimination with Matrices.
8
Elimination with Matrices
Elimination with Matrices
9
3. Multiplication and Inverse Matrices
3. Multiplication and Inverse Matrices
10
Inverse Matrices
Inverse Matrices
11
4. Factorization into A = LU
4. Factorization into A = LU
12
LU Decomposition
LU Decomposition
13
5. Transposes, Permutations, Spaces R^n
5. Transposes, Permutations, Spaces R^n
14
Subspaces of Three Dimensional Space
Subspaces of Three Dimensional Space
15
6. Column Space and Nullspace
6. Column Space and Nullspace
16
Vector Subspaces
Vector Subspaces
17
7. Solving Ax = 0: Pivot Variables, Special Solutions
7. Solving Ax = 0: Pivot Variables, Special Solutions
18
Solving Ax=0
Solving Ax=0
19
8. Solving Ax = b: Row Reduced Form R
8. Solving Ax = b: Row Reduced Form R
20
Solving Ax=b
Solving Ax=b
21
9. Independence, Basis, and Dimension
9. Independence, Basis, and Dimension
22
Basis and Dimension
Basis and Dimension
23
10. The Four Fundamental Subspaces
10. The Four Fundamental Subspaces
24
Computing the Four Fundamental Subspaces
Computing the Four Fundamental Subspaces
25
11. Matrix Spaces; Rank 1; Small World Graphs
11. Matrix Spaces; Rank 1; Small World Graphs
26
Matrix Spaces
Matrix Spaces
27
12. Graphs, Networks, Incidence Matrices
12. Graphs, Networks, Incidence Matrices
28
Graphs and Networks
Graphs and Networks
29
13. Quiz 1 Review
13. Quiz 1 Review
30
Exam #1 Problem Solving
Exam #1 Problem Solving
31
14. Orthogonal Vectors and Subspaces
14. Orthogonal Vectors and Subspaces
32
Orthogonal Vectors and Subspaces
Orthogonal Vectors and Subspaces
33
15. Projections onto Subspaces
15. Projections onto Subspaces
34
Projection into Subspaces
Projection into Subspaces
35
16. Projection Matrices and Least Squares
16. Projection Matrices and Least Squares
36
Least Squares Approximation
Least Squares Approximation
37
17. Orthogonal Matrices and Gram-Schmidt
17. Orthogonal Matrices and Gram-Schmidt
38
Gram-Schmidt Orthogonalization
Gram-Schmidt Orthogonalization
39
18. Properties of Determinants
18. Properties of Determinants
40
Properties of Determinants
Properties of Determinants
41
19. Determinant Formulas and Cofactors
19. Determinant Formulas and Cofactors
42
Determinants
Determinants
43
20. Cramer's Rule, Inverse Matrix, and Volume
20. Cramer's Rule, Inverse Matrix, and Volume
44
Determinants and Volume
Determinants and Volume
45
21. Eigenvalues and Eigenvectors
21. Eigenvalues and Eigenvectors
46
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
47
22. Diagonalization and Powers of A
22. Diagonalization and Powers of A
48
Powers of a Matrix
Powers of a Matrix
49
23. Differential Equations and exp(At)
23. Differential Equations and exp(At)
50
Differential Equations and exp (At)
Differential Equations and exp (At)
51
24. Markov Matrices; Fourier Series
24. Markov Matrices; Fourier Series
52
Markov Matrices
Markov Matrices
53
24b. Quiz 2 Review
24b. Quiz 2 Review
54
Exam #2 Problem Solving
Exam #2 Problem Solving
55
25. Symmetric Matrices and Positive Definiteness
25. Symmetric Matrices and Positive Definiteness
56
Symmetric Matrices and Positive Definiteness
Symmetric Matrices and Positive Definiteness
57
26. Complex Matrices; Fast Fourier Transform
26. Complex Matrices; Fast Fourier Transform
58
Complex Matrices
Complex Matrices
59
27. Positive Definite Matrices and Minima
27. Positive Definite Matrices and Minima
60
Positive Definite Matrices and Minima
Positive Definite Matrices and Minima
61
28. Similar Matrices and Jordan Form
28. Similar Matrices and Jordan Form
62
Similar Matrices
Similar Matrices
63
29. Singular Value Decomposition
29. Singular Value Decomposition
64
Computing the Singular Value Decomposition
Computing the Singular Value Decomposition
65
30. Linear Transformations and Their Matrices
30. Linear Transformations and Their Matrices
66
Linear Transformations
Linear Transformations
67
31. Change of Basis; Image Compression
31. Change of Basis; Image Compression
68
Change of Basis
Change of Basis
69
33. Left and Right Inverses; Pseudoinverse
33. Left and Right Inverses; Pseudoinverse
70
Pseudoinverses
Pseudoinverses
71
32. Quiz 3 Review
32. Quiz 3 Review
72
Exam #3 Problem Solving
Exam #3 Problem Solving
73
34. Final Course Review
34. Final Course Review
74
Final Exam Problem Solving
Final Exam Problem Solving