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    What is linear algebra?
  • Урок 2. 00:05:58
    Linear algebra applications
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    An enticing start to a linear algebra course!
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    How best to learn from this course
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    Maximizing your Udemy experience
  • Урок 6. 00:07:31
    Using MATLAB, Octave, or Python in this course
  • Урок 7. 00:12:46
    Algebraic and geometric interpretations of vectors
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    Vector addition and subtraction
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    Vector-scalar multiplication
  • Урок 10. 00:10:12
    Vector-vector multiplication: the dot product
  • Урок 11. 00:18:56
    Dot product properties: associative, distributive, commutative
  • Урок 12. 00:08:46
    Code challenge: dot products with matrix columns
  • Урок 13. 00:06:43
    Vector length
  • Урок 14. 00:23:39
    Dot product geometry: sign and orthogonality
  • Урок 15. 00:12:06
    Code challenge: dot product sign and scalar multiplication
  • Урок 16. 00:09:33
    Code challenge: is the dot product commutative?
  • Урок 17. 00:03:44
    Vector Hadamard multiplication
  • Урок 18. 00:10:18
    Outer product
  • Урок 19. 00:09:06
    Vector cross product
  • Урок 20. 00:08:18
    Vectors with complex numbers
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    Hermitian transpose (a.k.a. conjugate transpose)
  • Урок 22. 00:07:59
    Interpreting and creating unit vectors
  • Урок 23. 00:13:34
    Code challenge: dot products with unit vectors
  • Урок 24. 00:07:55
    Dimensions and fields in linear algebra
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    Subspaces
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    Subspaces vs. subsets
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    Span
  • Урок 28. 00:15:35
    Linear independence
  • Урок 29. 00:11:52
    Basis
  • Урок 30. 00:08:15
    Matrix terminology and dimensionality
  • Урок 31. 00:17:20
    A zoo of matrices
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    Matrix addition and subtraction
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    Matrix-scalar multiplication
  • Урок 34. 00:07:29
    Code challenge: is matrix-scalar multiplication a linear operation?
  • Урок 35. 00:10:25
    Transpose
  • Урок 36. 00:01:52
    Complex matrices
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    Diagonal and trace
  • Урок 38. 00:09:38
    Code challenge: linearity of trace
  • Урок 39. 00:14:14
    Broadcasting matrix arithmetic
  • Урок 40. 00:10:28
    Introduction to standard matrix multiplication
  • Урок 41. 00:11:56
    Four ways to think about matrix multiplication
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    Code challenge: matrix multiplication by layering
  • Урок 43. 00:03:43
    Matrix multiplication with a diagonal matrix
  • Урок 44. 00:08:16
    Order-of-operations on matrices
  • Урок 45. 00:16:44
    Matrix-vector multiplication
  • Урок 46. 00:15:33
    2D transformation matrices
  • Урок 47. 00:12:39
    Code challenge: Pure and impure rotation matrices
  • Урок 48. 00:15:59
    Code challenge: Geometric transformations via matrix multiplications
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    Additive and multiplicative matrix identities
  • Урок 50. 00:15:17
    Additive and multiplicative symmetric matrices
  • Урок 51. 00:05:01
    Hadamard (element-wise) multiplication
  • Урок 52. 00:12:04
    Code challenge: symmetry of combined symmetric matrices
  • Урок 53. 00:13:22
    Multiplication of two symmetric matrices
  • Урок 54. 00:06:28
    Code challenge: standard and Hadamard multiplication for diagonal matrices
  • Урок 55. 00:11:21
    Code challenge: Fourier transform via matrix multiplication!
  • Урок 56. 00:11:17
    Frobenius dot product
  • Урок 57. 00:18:12
    Matrix norms
  • Урок 58. 00:11:53
    Code challenge: conditions for self-adjoint
  • Урок 59. 00:04:25
    What about matrix division?
  • Урок 60. 00:10:51
    Rank: concepts, terms, and applications
  • Урок 61. 00:23:02
    Computing rank: theory and practice
  • Урок 62. 00:11:47
    Rank of added and multiplied matrices
  • Урок 63. 00:10:39
    Code challenge: reduced-rank matrix via multiplication
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    Code challenge: scalar multiplication and rank
  • Урок 65. 00:10:42
    Rank of A^TA and AA^T
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    Code challenge: rank of multiplied and summed matrices
  • Урок 67. 00:14:13
    Making a matrix full-rank by "shifting"
  • Урок 68. 00:11:47
    Code challenge: is this vector in the span of this set?
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    Course tangent: self-accountability in online learning
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    Column space of a matrix
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    Column space, visualized in code
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    Row space of a matrix
  • Урок 73. 00:14:40
    Null space and left null space of a matrix
  • Урок 74. 00:10:48
    Column/left-null and row/null spaces are orthogonal
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    Dimensions of column/row/null spaces
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    Example of the four subspaces
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    More on Ax=b and Ax=0
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    Systems of equations: algebra and geometry
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    Converting systems of equations to matrix equations
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    Gaussian elimination
  • Урок 81. 00:07:22
    Echelon form and pivots
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    Reduced row echelon form
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    Code challenge: RREF of matrices with different sizes and ranks
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    Matrix spaces after row reduction
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    Determinant: concept and applications
  • Урок 86. 00:07:04
    Determinant of a 2x2 matrix
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    Code challenge: determinant of small and large singular matrices
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    Determinant of a 3x3 matrix
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    Code challenge: large matrices with row exchanges
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    Find matrix values for a given determinant
  • Урок 91. 00:18:28
    Code challenge: determinant of shifted matrices
  • Урок 92. 00:10:38
    Code challenge: determinant of matrix product
  • Урок 93. 00:12:41
    Matrix inverse: Concept and applications
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    Computing the inverse in code
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    Inverse of a 2x2 matrix
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    The MCA algorithm to compute the inverse
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    Code challenge: Implement the MCA algorithm!!
  • Урок 98. 00:16:41
    Computing the inverse via row reduction
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    Code challenge: inverse of a diagonal matrix
  • Урок 100. 00:10:15
    Left inverse and right inverse
  • Урок 101. 00:12:41
    One-sided inverses in code
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    Proof: the inverse is unique
  • Урок 103. 00:11:35
    Pseudo-inverse, part 1
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    Code challenge: pseudoinverse of invertible matrices
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    Projections in R^2
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    Projections in R^N
  • Урок 107. 00:12:39
    Orthogonal and parallel vector components
  • Урок 108. 00:16:41
    Code challenge: decompose vector to orthogonal components
  • Урок 109. 00:12:03
    Orthogonal matrices
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    Gram-Schmidt procedure
  • Урок 111. 00:21:00
    QR decomposition
  • Урок 112. 00:20:36
    Code challenge: Gram-Schmidt algorithm
  • Урок 113. 00:01:46
    Matrix inverse via QR decomposition
  • Урок 114. 00:14:20
    Code challenge: Inverse via QR
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    Code challenge: Prove and demonstrate the Sherman-Morrison inverse
  • Урок 116. 00:06:01
    Code challenge: A^TA = R^TR
  • Урок 117. 00:13:13
    Introduction to least-squares
  • Урок 118. 00:10:08
    Least-squares via left inverse
  • Урок 119. 00:09:19
    Least-squares via orthogonal projection
  • Урок 120. 00:18:21
    Least-squares via row-reduction
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    Model-predicted values and residuals
  • Урок 122. 00:18:47
    Least-squares application 1
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    Least-squares application 2
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    Code challenge: Least-squares via QR decomposition
  • Урок 125. 00:12:53
    What are eigenvalues and eigenvectors?
  • Урок 126. 00:20:44
    Finding eigenvalues
  • Урок 127. 00:02:54
    Shortcut for eigenvalues of a 2x2 matrix
  • Урок 128. 00:14:25
    Code challenge: eigenvalues of diagonal and triangular matrices
  • Урок 129. 00:11:05
    Code challenge: eigenvalues of random matrices
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    Finding eigenvectors
  • Урок 131. 00:09:28
    Eigendecomposition by hand: two examples
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    Diagonalization
  • Урок 133. 00:20:37
    Matrix powers via diagonalization
  • Урок 134. 00:18:15
    Code challenge: eigendecomposition of matrix differences
  • Урок 135. 00:08:15
    Eigenvectors of distinct eigenvalues
  • Урок 136. 00:12:16
    Eigenvectors of repeated eigenvalues
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    Eigendecomposition of symmetric matrices
  • Урок 138. 00:07:20
    Eigenlayers of a matrix
  • Урок 139. 00:20:11
    Code challenge: reconstruct a matrix from eigenlayers
  • Урок 140. 00:05:00
    Eigendecomposition of singular matrices
  • Урок 141. 00:10:57
    Code challenge: trace and determinant, eigenvalues sum and product
  • Урок 142. 00:12:31
    Generalized eigendecomposition
  • Урок 143. 00:21:10
    Code challenge: GED in small and large matrices
  • Урок 144. 00:18:41
    Singular value decomposition (SVD)
  • Урок 145. 00:24:32
    Code challenge: SVD vs. eigendecomposition for square symmetric matrices
  • Урок 146. 00:13:04
    Relation between singular values and eigenvalues
  • Урок 147. 00:18:24
    Code challenge: U from eigendecomposition of A^TA
  • Урок 148. 00:14:34
    Code challenge: A^TA, Av, and singular vectors
  • Урок 149. 00:07:35
    SVD and the four subspaces
  • Урок 150. 00:21:57
    Spectral theory of matrices
  • Урок 151. 00:16:43
    SVD for low-rank approximations
  • Урок 152. 00:15:26
    Convert singular values to percent variance
  • Урок 153. 00:12:04
    Code challenge: When is UV^T valid, what is its norm, and is it orthogonal?
  • Урок 154. 00:13:30
    SVD, matrix inverse, and pseudoinverse
  • Урок 155. 00:12:48
    Condition number of a matrix
  • Урок 156. 00:15:09
    Code challenge: Create matrix with desired condition number
  • Урок 157. 00:15:28
    The quadratic form in algebra
  • Урок 158. 00:15:36
    The quadratic form in geometry
  • Урок 159. 00:06:36
    The normalized quadratic form
  • Урок 160. 00:16:21
    Code challenge: Visualize the normalized quadratic form
  • Урок 161. 00:06:18
    Eigenvectors and the quadratic form surface
  • Урок 162. 00:29:02
    Application of the normalized quadratic form: PCA
  • Урок 163. 00:17:34
    Quadratic form of generalized eigendecomposition
  • Урок 164. 00:12:55
    Matrix definiteness, geometry, and eigenvalues
  • Урок 165. 00:06:52
    Proof: A^TA is always positive (semi)definite
  • Урок 166. 00:07:16
    Proof: Eigenvalues and matrix definiteness
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