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  1. Урок 1. 00:04:41
    What we'll learn in this course
  2. Урок 2. 00:01:27
    How to get the most out of this course
  3. Урок 3. 00:01:25
    Introduction to operations on one matrix
  4. Урок 4. 00:12:16
    Linear systems in two unknowns
  5. Урок 5. 00:10:21
    Linear systems in three unknowns
  6. Урок 6. 00:06:08
    Matrix dimensions and entries
  7. Урок 7. 00:09:59
    Representing systems with matrices
  8. Урок 8. 00:10:15
    Simple row operations
  9. Урок 9. 00:16:19
    Pivot entries and row-echelon forms
  10. Урок 10. 00:13:57
    Gauss-Jordan elimination
  11. Урок 11. 00:13:21
    Number of solutions to the linear system
  12. Урок 12. 00:01:18
    Introduction to operations on two matrices
  13. Урок 13. 00:09:49
    Matrix addition and subtraction
  14. Урок 14. 00:06:06
    Scalar multiplication
  15. Урок 15. 00:04:07
    Zero matrices
  16. Урок 16. 00:11:52
    Matrix multiplication
  17. Урок 17. 00:09:24
    Identity matrices
  18. Урок 18. 00:13:20
    The elimination matrix
  19. Урок 19. 00:01:18
    Introduction to matrices as vectors
  20. Урок 20. 00:08:55
    Vectors
  21. Урок 21. 00:10:50
    Vector operations
  22. Урок 22. 00:16:11
    Unit vectors and basis vectors
  23. Урок 23. 00:13:29
    Linear combinations and span
  24. Урок 24. 00:13:56
    Linear independence in two dimensions
  25. Урок 25. 00:09:39
    Linear independence in three dimensions
  26. Урок 26. 00:13:39
    Linear subspaces
  27. Урок 27. 00:09:23
    Spans as subspaces
  28. Урок 28. 00:17:16
    Basis
  29. Урок 29. 00:01:12
    Introduction to dot products and cross products
  30. Урок 30. 00:10:36
    Dot products
  31. Урок 31. 00:08:06
    Cauchy-Schwarz inequality
  32. Урок 32. 00:10:28
    Vector triangle inequality
  33. Урок 33. 00:09:06
    Angle between vectors
  34. Урок 34. 00:09:10
    Equation of a plane, and normal vectors
  35. Урок 35. 00:14:24
    Cross products
  36. Урок 36. 00:13:39
    Dot and cross products as opposite ideas
  37. Урок 37. 00:01:10
    Introduction to matrix-vector products
  38. Урок 38. 00:08:33
    Multiplying matrices by vectors
  39. Урок 39. 00:20:25
    The null space and Ax=O
  40. Урок 40. 00:16:21
    Null space of a matrix
  41. Урок 41. 00:17:18
    The column space and Ax=b
  42. Урок 42. 00:16:47
    Solving Ax=b
  43. Урок 43. 00:09:41
    Dimensionality, nullity, and rank
  44. Урок 44. 00:01:23
    Introduction to transformations
  45. Урок 45. 00:12:43
    Functions and transformations
  46. Урок 46. 00:19:29
    Transformation matrices and the image of the subset
  47. Урок 47. 00:10:16
    Preimage, image, and the kernel
  48. Урок 48. 00:14:50
    Linear transformations as matrix-vector products
  49. Урок 49. 00:05:50
    Linear transformations as rotations
  50. Урок 50. 00:09:30
    Adding and scaling linear transformations
  51. Урок 51. 00:15:53
    Projections as linear transformations
  52. Урок 52. 00:10:01
    Compositions of linear transformations
  53. Урок 53. 00:01:28
    Introduction to inverses
  54. Урок 54. 00:14:40
    Inverse of a transformation
  55. Урок 55. 00:18:20
    Invertibility from the matrix-vector product
  56. Урок 56. 00:09:55
    Inverse transformations are linear
  57. Урок 57. 00:11:37
    Matrix inverses, and invertible and singular matrices
  58. Урок 58. 00:08:40
    Solving systems with inverse matrices
  59. Урок 59. 00:00:56
    Introduction to determinants
  60. Урок 60. 00:20:22
    Determinants
  61. Урок 61. 00:15:48
    Cramer's rule for solving systems
  62. Урок 62. 00:09:53
    Modifying determinants
  63. Урок 63. 00:17:00
    Upper and lower triangular matrices
  64. Урок 64. 00:08:29
    Using determinants to find area
  65. Урок 65. 00:00:59
    Introduction to transposes
  66. Урок 66. 00:09:15
    Transposes and their determinants
  67. Урок 67. 00:12:40
    Transposes of products, sums, and inverses
  68. Урок 68. 00:21:22
    Null and column spaces of the transpose
  69. Урок 69. 00:07:05
    The product of a matrix and its transpose
  70. Урок 70. 00:01:30
    Introduction to orthogonality and change of basis
  71. Урок 71. 00:15:36
    Orthogonal complements
  72. Урок 72. 00:15:50
    Orthogonal complements of the fundamental subspaces
  73. Урок 73. 00:18:37
    Projection onto the subspace
  74. Урок 74. 00:18:53
    Least squares solution
  75. Урок 75. 00:15:33
    Coordinates in a new basis
  76. Урок 76. 00:14:33
    Transformation matrix for a basis
  77. Урок 77. 00:01:10
    Introduction to orthonormal bases and Gram-Schmidt
  78. Урок 78. 00:09:50
    Orthonormal bases
  79. Урок 79. 00:09:07
    Projection onto an orthonormal basis
  80. Урок 80. 00:16:57
    Gram-Schmidt process for change of basis
  81. Урок 81. 00:00:57
    Introduction to Eigenvalues and Eigenvectors
  82. Урок 82. 00:21:34
    Eigenvalues, eigenvectors, eigenspaces
  83. Урок 83. 00:16:10
    Eigen in three dimensions
  84. Урок 84. 00:00:26
    Wrap-up