Learn · Linear Algebra

Lecture 9 of 35Video Lectures51 min

Lecture 9: Independence, basis, and dimension

Prof. Gilbert Strang · Massachusetts Institute of Technology

At MIT OpenCourseWare Transcript

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From
Linear Algebra, Massachusetts Institute of Technology (at MIT OpenCourseWare)
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only.
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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All the 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