Complete linear algebra theory and implementation

1. Complete linear algebra theory and implementation/11. Least-squares for model-fitting in statistics/8. Least-squares application 2.mp4133.28MB
2. Complete linear algebra theory and implementation/1. Introductions/1. What is linear algebra.mp447.12MB
3. Complete linear algebra theory and implementation/1. Introductions/2. Linear algebra applications.mp430.65MB
4. Complete linear algebra theory and implementation/1. Introductions/3. How best to learn from this course.mp422.52MB
5. Complete linear algebra theory and implementation/1. Introductions/4. Using Jupyter online for Python code (no installation necessary!).mp423.01MB
6. Complete linear algebra theory and implementation/1. Introductions/5. Leaving reviews, course coupons.mp417.85MB
7. Complete linear algebra theory and implementation/2. Vectors/2. Algebraic and geometric interpretations of vectors.mp452.01MB
8. Complete linear algebra theory and implementation/2. Vectors/3. Vector addition and subtraction.mp429.49MB
9. Complete linear algebra theory and implementation/2. Vectors/4. Vector-scalar multiplication.mp433.98MB
10. Complete linear algebra theory and implementation/2. Vectors/5. Vector-vector multiplication the dot product.mp440.14MB
11. Complete linear algebra theory and implementation/2. Vectors/6. Vector length.mp423.28MB
12. Complete linear algebra theory and implementation/2. Vectors/8. Dot product geometry sign and orthogonality.mp471.23MB
13. Complete linear algebra theory and implementation/2. Vectors/11. Code challenge dot product sign and scalar multiplication.mp438.03MB
14. Complete linear algebra theory and implementation/2. Vectors/12. Code challenge is the dot product commutative.mp427.53MB
15. Complete linear algebra theory and implementation/2. Vectors/13. Outer product.mp429.42MB
16. Complete linear algebra theory and implementation/2. Vectors/14. Vectors with complex numbers.mp431.88MB
17. Complete linear algebra theory and implementation/2. Vectors/15. Hermitian transpose (a.k.a. conjugate transpose).mp444.89MB
18. Complete linear algebra theory and implementation/2. Vectors/16. Interpreting and creating unit vectors.mp421.84MB
19. Complete linear algebra theory and implementation/2. Vectors/17. Code challenge dot products with unit vectors.mp435.31MB
20. Complete linear algebra theory and implementation/2. Vectors/18. Dimensions and fields in linear algebra.mp437.59MB
21. Complete linear algebra theory and implementation/2. Vectors/19. Subspaces.mp466.72MB
22. Complete linear algebra theory and implementation/2. Vectors/20. Subspaces vs. subsets.mp426.26MB
23. Complete linear algebra theory and implementation/2. Vectors/21. Span.mp460.75MB
24. Complete linear algebra theory and implementation/2. Vectors/23. Linear independence.mp472.1MB
25. Complete linear algebra theory and implementation/2. Vectors/24. Basis.mp443.9MB
26. Complete linear algebra theory and implementation/3. Introduction to matrices/2. Matrix terminology and dimensionality.mp428.51MB
27. Complete linear algebra theory and implementation/3. Introduction to matrices/4. A zoo of matrices.mp445.64MB
28. Complete linear algebra theory and implementation/3. Introduction to matrices/6. Matrix addition and subtraction.mp419.26MB
29. Complete linear algebra theory and implementation/3. Introduction to matrices/7. Matrix-scalar multiplication.mp47.97MB
30. Complete linear algebra theory and implementation/3. Introduction to matrices/8. Code challenge is matrix-scalar multiplication a linear operation.mp418.26MB
31. Complete linear algebra theory and implementation/3. Introduction to matrices/9. Transpose.mp427.63MB
32. Complete linear algebra theory and implementation/3. Introduction to matrices/10. Complex matrices.mp46.76MB
33. Complete linear algebra theory and implementation/3. Introduction to matrices/12. Diagonal and trace.mp422.22MB
34. Complete linear algebra theory and implementation/3. Introduction to matrices/13. Code challenge linearity of trace.mp429.57MB
35. Complete linear algebra theory and implementation/4. Matrix multiplications/2. Introduction to standard matrix multiplication.mp429.84MB
36. Complete linear algebra theory and implementation/4. Matrix multiplications/3. Four ways to think about matrix multiplication.mp437.76MB
37. Complete linear algebra theory and implementation/4. Matrix multiplications/4. Code challenge matrix multiplication by layering.mp425.33MB
38. Complete linear algebra theory and implementation/4. Matrix multiplications/5. Matrix multiplication with a diagonal matrix.mp413.07MB
39. Complete linear algebra theory and implementation/4. Matrix multiplications/6. Order-of-operations on matrices.mp433.51MB
40. Complete linear algebra theory and implementation/4. Matrix multiplications/7. Matrix-vector multiplication.mp444.23MB
41. Complete linear algebra theory and implementation/4. Matrix multiplications/9. 2D transformation matrices.mp455.57MB
42. Complete linear algebra theory and implementation/4. Matrix multiplications/10. Additive and multiplicative matrix identities.mp420.78MB
43. Complete linear algebra theory and implementation/4. Matrix multiplications/11. Additive and multiplicative symmetric matrices.mp448.58MB
44. Complete linear algebra theory and implementation/4. Matrix multiplications/12. Hadamard (element-wise) multiplication.mp48.66MB
45. Complete linear algebra theory and implementation/4. Matrix multiplications/14. Code challenge symmetry of combined symmetric matrices.mp434.19MB
46. Complete linear algebra theory and implementation/4. Matrix multiplications/15. Multiplication of two symmetric matrices.mp434.5MB
47. Complete linear algebra theory and implementation/4. Matrix multiplications/16. Code challenge standard and Hadamard multiplication for diagonal matrices.mp414.24MB
48. Complete linear algebra theory and implementation/4. Matrix multiplications/17. Frobenius dot product.mp437.25MB
49. Complete linear algebra theory and implementation/4. Matrix multiplications/18. What about matrix division.mp414.57MB
50. Complete linear algebra theory and implementation/5. Matrix rank/2. Rank concepts, terms, and applications.mp449.23MB
51. Complete linear algebra theory and implementation/5. Matrix rank/4. Computing rank theory and practice.mp468.72MB
52. Complete linear algebra theory and implementation/5. Matrix rank/5. Rank of added and multiplied matrices.mp455.09MB
53. Complete linear algebra theory and implementation/5. Matrix rank/7. Code challenge reduced-rank matrix via multiplication.mp417.34MB
54. Complete linear algebra theory and implementation/5. Matrix rank/8. Rank of A^TA and AA^T.mp439.64MB
55. Complete linear algebra theory and implementation/5. Matrix rank/9. Code challenge scalar multiplication and rank.mp430.29MB
56. Complete linear algebra theory and implementation/5. Matrix rank/10. Code challenge rank of multiplied and summed matrices.mp427.11MB
57. Complete linear algebra theory and implementation/5. Matrix rank/11. Making a matrix full-rank by shifting.mp437.79MB
58. Complete linear algebra theory and implementation/5. Matrix rank/12. Code challenge is this vector in the span of this set.mp425.11MB
59. Complete linear algebra theory and implementation/6. Matrix spaces/2. Column space of a matrix.mp472MB
60. Complete linear algebra theory and implementation/6. Matrix spaces/3. Row space of a matrix.mp419.3MB
61. Complete linear algebra theory and implementation/6. Matrix spaces/4. Null space and left null space of a matrix.mp464.13MB
62. Complete linear algebra theory and implementation/6. Matrix spaces/5. Columnleft-null and rownull spaces are orthogonal.mp430.98MB
63. Complete linear algebra theory and implementation/6. Matrix spaces/6. Dimensions of columnrownull spaces.mp426.84MB
64. Complete linear algebra theory and implementation/6. Matrix spaces/7. Example of the four subspaces.mp450.25MB
65. Complete linear algebra theory and implementation/6. Matrix spaces/8. More on Ax=b and Ax=0.mp428.47MB
66. Complete linear algebra theory and implementation/7. Solving systems of equations/2. Systems of equations algebra and geometry.mp485.04MB
67. Complete linear algebra theory and implementation/7. Solving systems of equations/3. Converting systems of equations to matrix equations.mp429.44MB
68. Complete linear algebra theory and implementation/7. Solving systems of equations/4. Gaussian elimination.mp461.62MB
69. Complete linear algebra theory and implementation/7. Solving systems of equations/5. Echelon form and pivots.mp426.42MB
70. Complete linear algebra theory and implementation/7. Solving systems of equations/6. Reduced row echelon form.mp461.34MB
71. Complete linear algebra theory and implementation/7. Solving systems of equations/7. Code challenge RREF of matrices with different sizes and ranks.mp439.28MB
72. Complete linear algebra theory and implementation/7. Solving systems of equations/8. Matrix spaces after row reduction.mp439.52MB
73. Complete linear algebra theory and implementation/8. Matrix determinant/2. Determinant concept and applications.mp441.46MB
74. Complete linear algebra theory and implementation/8. Matrix determinant/3. Code challenge determinant of small and large singular matrices.mp425.03MB
75. Complete linear algebra theory and implementation/8. Matrix determinant/4. Determinant of a 2x2 matrix.mp427.45MB
76. Complete linear algebra theory and implementation/8. Matrix determinant/5. Determinant of a 3x3 matrix.mp451.56MB
77. Complete linear algebra theory and implementation/8. Matrix determinant/6. Code challenge determinant of shifted matrices.mp462.47MB
78. Complete linear algebra theory and implementation/8. Matrix determinant/7. Find matrix values for a given determinant.mp420.59MB
79. Complete linear algebra theory and implementation/9. Matrix inverse/2. Matrix inverse Concept and applications.mp441.8MB
80. Complete linear algebra theory and implementation/9. Matrix inverse/3. Inverse of a 2x2 matrix.mp426.54MB
81. Complete linear algebra theory and implementation/9. Matrix inverse/4. The MCA algorithm to compute the inverse.mp452.45MB
82. Complete linear algebra theory and implementation/9. Matrix inverse/5. Computing the inverse via row reduction.mp485.53MB
83. Complete linear algebra theory and implementation/9. Matrix inverse/6. Code challenge inverse of a diagonal matrix.mp437.18MB
84. Complete linear algebra theory and implementation/9. Matrix inverse/7. Left inverse and right inverse.mp476.67MB
85. Complete linear algebra theory and implementation/9. Matrix inverse/8. Proof the inverse is unique.mp414.05MB
86. Complete linear algebra theory and implementation/9. Matrix inverse/9. Pseudo-inverse, part 1.mp456.05MB
87. Complete linear algebra theory and implementation/9. Matrix inverse/10. Code challenge pseudoinverse of invertible matrices.mp413.36MB
88. Complete linear algebra theory and implementation/10. Projections and orthogonalization/2. Projections in R^2.mp443.89MB
89. Complete linear algebra theory and implementation/10. Projections and orthogonalization/3. Projections in R^N.mp475.55MB
90. Complete linear algebra theory and implementation/10. Projections and orthogonalization/4. Orthogonal and parallel vector components.mp447.43MB
91. Complete linear algebra theory and implementation/10. Projections and orthogonalization/5. Code challenge decompose vector to orthogonal components.mp447.56MB
92. Complete linear algebra theory and implementation/10. Projections and orthogonalization/6. Orthogonal matrices.mp455.44MB
93. Complete linear algebra theory and implementation/10. Projections and orthogonalization/7. Gram-Schmidt and QR decomposition.mp467.62MB
94. Complete linear algebra theory and implementation/10. Projections and orthogonalization/8. Matrix inverse via QR decomposition.mp413.39MB
95. Complete linear algebra theory and implementation/10. Projections and orthogonalization/9. Code challenge Inverse via QR.mp447.84MB
96. Complete linear algebra theory and implementation/11. Least-squares for model-fitting in statistics/2. Introduction to least-squares.mp479.62MB
97. Complete linear algebra theory and implementation/11. Least-squares for model-fitting in statistics/3. Least-squares via left inverse.mp449.1MB
98. Complete linear algebra theory and implementation/11. Least-squares for model-fitting in statistics/4. Least-squares via orthogonal projection.mp434.75MB
99. Complete linear algebra theory and implementation/11. Least-squares for model-fitting in statistics/5. Least-squares via row-reduction.mp446.89MB
100. Complete linear algebra theory and implementation/11. Least-squares for model-fitting in statistics/6. Model-predicted values and residuals.mp430.92MB
101. Complete linear algebra theory and implementation/11. Least-squares for model-fitting in statistics/7. Least-squares application 1.mp481.33MB
102. Complete linear algebra theory and implementation/12. Eigendecomposition/2. What are eigenvalues and eigenvectors.mp470.3MB
103. Complete linear algebra theory and implementation/12. Eigendecomposition/3. Finding eigenvalues.mp473.11MB
104. Complete linear algebra theory and implementation/12. Eigendecomposition/4. Shortcut for eigenvalues of a 2x2 matrix.mp48.64MB
105. Complete linear algebra theory and implementation/12. Eigendecomposition/5. Code challenge eigenvalues of diagonal and triangular matrices.mp425.62MB
106. Complete linear algebra theory and implementation/12. Eigendecomposition/6. Code challenge eigenvalues of random matrices.mp439.63MB
107. Complete linear algebra theory and implementation/12. Eigendecomposition/7. Finding eigenvectors.mp464.81MB
108. Complete linear algebra theory and implementation/12. Eigendecomposition/8. Eigendecomposition by hand two examples.mp451.83MB
109. Complete linear algebra theory and implementation/12. Eigendecomposition/9. Diagonalization.mp447.37MB
110. Complete linear algebra theory and implementation/12. Eigendecomposition/10. Matrix powers via diagonalization.mp499.59MB
111. Complete linear algebra theory and implementation/12. Eigendecomposition/11. Eigenvectors of distinct eigenvalues.mp455.81MB
112. Complete linear algebra theory and implementation/12. Eigendecomposition/12. Eigenvectors of repeated eigenvalues.mp464.79MB
113. Complete linear algebra theory and implementation/12. Eigendecomposition/13. Eigendecomposition of symmetric matrices.mp473.8MB
114. Complete linear algebra theory and implementation/12. Eigendecomposition/14. Eigendecomposition of singular matrices.mp415.75MB
115. Complete linear algebra theory and implementation/12. Eigendecomposition/15. Code challenge trace and determinant, eigenvalues sum and product.mp424.11MB
116. Complete linear algebra theory and implementation/12. Eigendecomposition/16. Generalized eigendecomposition.mp461.91MB
117. Complete linear algebra theory and implementation/13. Singular value decomposition/2. Singular value decomposition (SVD).mp459.71MB
118. Complete linear algebra theory and implementation/13. Singular value decomposition/3. Code challenge SVD vs. eigendecomposition for square symmetric matrices.mp479.19MB
119. Complete linear algebra theory and implementation/13. Singular value decomposition/4. SVD and the four subspaces.mp437.51MB
120. Complete linear algebra theory and implementation/13. Singular value decomposition/5. Spectral theory of matrices.mp4116.58MB
121. Complete linear algebra theory and implementation/13. Singular value decomposition/6. SVD for low-rank approximations.mp467.66MB
122. Complete linear algebra theory and implementation/13. Singular value decomposition/7. Convert singular values to percent variance.mp472.94MB
123. Complete linear algebra theory and implementation/13. Singular value decomposition/8. SVD, matrix inverse, and pseudoinverse.mp449.77MB
124. Complete linear algebra theory and implementation/13. Singular value decomposition/9. Condition number of a matrix.mp452.99MB
125. Complete linear algebra theory and implementation/13. Singular value decomposition/10. Code challenge Create matrix with desired condition number.mp478.71MB
126. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/2. The quadratic form in algebra.mp451.31MB
127. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/3. The quadratic form in geometry.mp464.7MB
128. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/4. The normalized quadratic form.mp431.77MB
129. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/5. Code challenge Visualize the normalized quadratic form.mp481.33MB
130. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/6. Eigenvectors and the quadratic form surface.mp445.25MB
131. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/7. Application of the normalized quadratic form PCA.mp4131.56MB
132. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/8. Quadratic form of generalized eigendecomposition.mp465.29MB
133. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/9. Matrix definiteness, geometry, and eigenvalues.mp453.06MB
134. Complete linear algebra theory and implementation/14. Quadratic form and definiteness/10. Proof A^TA is always positive (semi)definite.mp431.34MB