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Linear Algebra

Linear Algebra

Prof. Gilbert Strang via MIT OpenCourseWare Direct link

6. Column Space and Nullspace

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6. Column Space and Nullspace

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Linear Algebra

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  1. 1 An Interview with Gilbert Strang on Teaching Linear Algebra
  2. 2 Course Introduction | MIT 18.06SC Linear Algebra
  3. 3 1. The Geometry of Linear Equations
  4. 4 Geometry of Linear Algebra
  5. 5 Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008
  6. 6 An Overview of Key Ideas
  7. 7 2. Elimination with Matrices.
  8. 8 Elimination with Matrices
  9. 9 3. Multiplication and Inverse Matrices
  10. 10 Inverse Matrices
  11. 11 4. Factorization into A = LU
  12. 12 LU Decomposition
  13. 13 5. Transposes, Permutations, Spaces R^n
  14. 14 Subspaces of Three Dimensional Space
  15. 15 6. Column Space and Nullspace
  16. 16 Vector Subspaces
  17. 17 7. Solving Ax = 0: Pivot Variables, Special Solutions
  18. 18 Solving Ax=0
  19. 19 8. Solving Ax = b: Row Reduced Form R
  20. 20 Solving Ax=b
  21. 21 9. Independence, Basis, and Dimension
  22. 22 Basis and Dimension
  23. 23 10. The Four Fundamental Subspaces
  24. 24 Computing the Four Fundamental Subspaces
  25. 25 11. Matrix Spaces; Rank 1; Small World Graphs
  26. 26 Matrix Spaces
  27. 27 12. Graphs, Networks, Incidence Matrices
  28. 28 Graphs and Networks
  29. 29 13. Quiz 1 Review
  30. 30 Exam #1 Problem Solving
  31. 31 14. Orthogonal Vectors and Subspaces
  32. 32 Orthogonal Vectors and Subspaces
  33. 33 15. Projections onto Subspaces
  34. 34 Projection into Subspaces
  35. 35 16. Projection Matrices and Least Squares
  36. 36 Least Squares Approximation
  37. 37 17. Orthogonal Matrices and Gram-Schmidt
  38. 38 Gram-Schmidt Orthogonalization
  39. 39 18. Properties of Determinants
  40. 40 Properties of Determinants
  41. 41 19. Determinant Formulas and Cofactors
  42. 42 Determinants
  43. 43 20. Cramer's Rule, Inverse Matrix, and Volume
  44. 44 Determinants and Volume
  45. 45 21. Eigenvalues and Eigenvectors
  46. 46 Eigenvalues and Eigenvectors
  47. 47 22. Diagonalization and Powers of A
  48. 48 Powers of a Matrix
  49. 49 23. Differential Equations and exp(At)
  50. 50 Differential Equations and exp (At)
  51. 51 24. Markov Matrices; Fourier Series
  52. 52 Markov Matrices
  53. 53 24b. Quiz 2 Review
  54. 54 Exam #2 Problem Solving
  55. 55 25. Symmetric Matrices and Positive Definiteness
  56. 56 Symmetric Matrices and Positive Definiteness
  57. 57 26. Complex Matrices; Fast Fourier Transform
  58. 58 Complex Matrices
  59. 59 27. Positive Definite Matrices and Minima
  60. 60 Positive Definite Matrices and Minima
  61. 61 28. Similar Matrices and Jordan Form
  62. 62 Similar Matrices
  63. 63 29. Singular Value Decomposition
  64. 64 Computing the Singular Value Decomposition
  65. 65 30. Linear Transformations and Their Matrices
  66. 66 Linear Transformations
  67. 67 31. Change of Basis; Image Compression
  68. 68 Change of Basis
  69. 69 33. Left and Right Inverses; Pseudoinverse
  70. 70 Pseudoinverses
  71. 71 32. Quiz 3 Review
  72. 72 Exam #3 Problem Solving
  73. 73 34. Final Course Review
  74. 74 Final Exam Problem Solving

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