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Course18.0635 lectures27 h 52 min

Linear Algebra

Prof. Gilbert Strang · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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.

Lectures

Video Lectures

  1. Lecture 1: The geometry of linear equations 40 min · Video
  2. Lecture 2: Elimination with matrices 48 min · Video
  3. Lecture 3: Multiplication and inverse matrices 47 min · Video
  4. Lecture 4: Factorization into A = LU 49 min · Video
  5. Lecture 5: Transposes, permutations, spaces R^n 48 min · Video
  6. Lecture 6: Column space and nullspace 47 min · Video
  7. Lecture 7: Solving Ax = 0: pivot variables, special solutions 44 min · Video
  8. Lecture 8: Solving Ax = b: row reduced form R 48 min · Video
  9. Lecture 9: Independence, basis, and dimension 51 min · Video
  10. Lecture 10: The four fundamental subspaces 50 min · Video
  11. Lecture 11: Matrix spaces; rank 1; small world graphs 46 min · Video
  12. Lecture 12: Graphs, networks, incidence matrices 48 min · Video
  13. Lecture 13: Quiz 1 review 48 min · Video
  14. Lecture 14: Orthogonal vectors and subspaces 50 min · Video
  15. Lecture 15: Projections onto subspaces 49 min · Video
  16. Lecture 16: Projection matrices and least squares 49 min · Video
  17. Lecture 17: Orthogonal matrices and Gram-Schmidt 50 min · Video
  18. Lecture 18: Properties of determinants 50 min · Video
  19. Lecture 19: Determinant formulas and cofactors 54 min · Video
  20. Lecture 20: Cramer's rule, inverse matrix, and volume 52 min · Video
  21. Lecture 21: Eigenvalues and eigenvectors 52 min · Video
  22. Lecture 22: Diagonalization and powers of A 52 min · Video
  23. Lecture 23: Differential equations and exp(At) 52 min · Video
  24. Lecture 24: Markov matrices; fourier series 52 min · Video
  25. Lecture 24b: Quiz 2 review 49 min · Video
  26. Lecture 25: Symmetric matrices and positive definiteness 44 min · Video
  27. Lecture 26: Complex matrices; fast fourier transform 48 min · Video
  28. Lecture 27: Positive definite matrices and minima 51 min · Video
  29. Lecture 28: Similar matrices and Jordan form 46 min · Video
  30. Lecture 29: Singular value decomposition 41 min · Video
  31. Lecture 30: Linear transformations and their matrices 50 min · Video
  32. Lecture 31: Change of basis; image compression 51 min · Video
  33. Lecture 32: Quiz 3 review 48 min · Video
  34. Lecture 33: Left and right inverses; pseudoinverse 42 min · Video
  35. Lecture 34: Final course review 44 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Mathematics
Teacher
Prof. Gilbert Strang
Term
Spring 2010
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Gilbert Strang. Linear Algebra. Spring 2010. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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