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18.06

Linear Algebra

Prof. Gilbert Strang | Spring 2010

Science & Math Mathematics Linear Algebra

前往原始課程

CC BY-NC-SA 4.0

課程簡介

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

Source	MIT 開放式課程
科系	Mathematics
Language	English
影片數	36

課程影片 (36)

An Interview with Gilbert Strang on Teaching Linear Algebra

1. The Geometry of Linear Equations

2. Elimination with Matrices.

3. Multiplication and Inverse Matrices

4. Factorization into A = LU

5. Transposes, Permutations, Spaces R^n

6. Column Space and Nullspace

7. Solving Ax = 0: Pivot Variables, Special Solutions

8. Solving Ax = b: Row Reduced Form R

9. Independence, Basis, and Dimension

10. The Four Fundamental Subspaces

11. Matrix Spaces; Rank 1; Small World Graphs

12. Graphs, Networks, Incidence Matrices

13. Quiz 1 Review

14. Orthogonal Vectors and Subspaces

15. Projections onto Subspaces

16. Projection Matrices and Least Squares

17. Orthogonal Matrices and Gram-Schmidt

18. Properties of Determinants

19. Determinant Formulas and Cofactors

20. Cramer's Rule, Inverse Matrix, and Volume

21. Eigenvalues and Eigenvectors

22. Diagonalization and Powers of A

23. Differential Equations and exp(At)

24. Markov Matrices; Fourier Series

24b. Quiz 2 Review

25. Symmetric Matrices and Positive Definiteness

26. Complex Matrices; Fast Fourier Transform

27. Positive Definite Matrices and Minima

28. Similar Matrices and Jordan Form

29. Singular Value Decomposition

30. Linear Transformations and Their Matrices

31. Change of Basis; Image Compression

32. Quiz 3 Review

33. Left and Right Inverses; Pseudoinverse

34. Final Course Review

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