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Uedu Open / Linear Algebra
18.06

Linear Algebra

Prof. Gilbert Strang | Spring 2010
Science & Math Mathematics Linear Algebra
Go to original course
CC BY-NC-SA 4.0
Course introduction
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Course Information
SourceMIT 開放式課程
DepartmentMathematics
LanguageEnglish
Number of videos36
Course videos (36)
1
An Interview with Gilbert Strang on Teaching Linear Algebra
An Interview with Gilbert Strang on Teaching Linear Algebra
2
1. The Geometry of Linear Equations
1. The Geometry of Linear Equations
3
2. Elimination with Matrices.
2. Elimination with Matrices.
4
3. Multiplication and Inverse Matrices
3. Multiplication and Inverse Matrices
5
4. Factorization into A = LU
4. Factorization into A = LU
6
5. Transposes, Permutations, Spaces R^n
5. Transposes, Permutations, Spaces R^n
7
6. Column Space and Nullspace
6. Column Space and Nullspace
8
7. Solving Ax = 0: Pivot Variables, Special Solutions
7. Solving Ax = 0: Pivot Variables, Special Solutions
9
8. Solving Ax = b: Row Reduced Form R
8. Solving Ax = b: Row Reduced Form R
10
9. Independence, Basis, and Dimension
9. Independence, Basis, and Dimension
11
10. The Four Fundamental Subspaces
10. The Four Fundamental Subspaces
12
11. Matrix Spaces; Rank 1; Small World Graphs
11. Matrix Spaces; Rank 1; Small World Graphs
13
12. Graphs, Networks, Incidence Matrices
12. Graphs, Networks, Incidence Matrices
14
13. Quiz 1 Review
13. Quiz 1 Review
15
14. Orthogonal Vectors and Subspaces
14. Orthogonal Vectors and Subspaces
16
15. Projections onto Subspaces
15. Projections onto Subspaces
17
16. Projection Matrices and Least Squares
16. Projection Matrices and Least Squares
18
17. Orthogonal Matrices and Gram-Schmidt
17. Orthogonal Matrices and Gram-Schmidt
19
18. Properties of Determinants
18. Properties of Determinants
20
19. Determinant Formulas and Cofactors
19. Determinant Formulas and Cofactors
21
20. Cramer's Rule, Inverse Matrix, and Volume
20. Cramer's Rule, Inverse Matrix, and Volume
22
21. Eigenvalues and Eigenvectors
21. Eigenvalues and Eigenvectors
23
22. Diagonalization and Powers of A
22. Diagonalization and Powers of A
24
23. Differential Equations and exp(At)
23. Differential Equations and exp(At)
25
24. Markov Matrices; Fourier Series
24. Markov Matrices; Fourier Series
26
24b. Quiz 2 Review
24b. Quiz 2 Review
27
25. Symmetric Matrices and Positive Definiteness
25. Symmetric Matrices and Positive Definiteness
28
26. Complex Matrices; Fast Fourier Transform
26. Complex Matrices; Fast Fourier Transform
29
27. Positive Definite Matrices and Minima
27. Positive Definite Matrices and Minima
30
28. Similar Matrices and Jordan Form
28. Similar Matrices and Jordan Form
31
29. Singular Value Decomposition
29. Singular Value Decomposition
32
30. Linear Transformations and Their Matrices
30. Linear Transformations and Their Matrices
33
31. Change of Basis; Image Compression
31. Change of Basis; Image Compression
34
32. Quiz 3 Review
32. Quiz 3 Review
35
33. Left and Right Inverses; Pseudoinverse
33. Left and Right Inverses; Pseudoinverse
36
34. Final Course Review
34. Final Course Review