# Linear Algebra

- Institution: Massachusetts Institute of Technology
- Department: Mathematics
- Teacher: Prof. Gilbert Strang
- Term: Fall 2011
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [MIT OpenCourseWare](https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/)
- Licence: [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) (Non-commercial use only.)
- Syllabus: [at the source](https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/pages/syllabus/)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

A complete set of Lecture Videos by Professor Gilbert Strang.

Summary Notes for all videos along with suggested readings in Prof. Strang’s textbook Linear Algebra.

Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.

Problem Sets to do on your own with Solutions to check your answers against when you’re done.

A selection of Java® Demonstrations to illustrate key concepts.

A full set of Exams with Solutions, including review material to help you prepare.

## Lectures

1. [Linear Algebra Course Introduction](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/b8d2630458d4), 8 min (Video)
2. [An Interview with Gilbert Strang on Teaching Linear Algebra](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/099909cfd49b), 8 min (Video)
3. [The Geometry of Linear Equations](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/8fc6d51e610c), 40 min (Video)
4. [Geometry of Linear Algebra](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/112e14589a3c), 17 min (Video)
5. [线性代数的几何表示](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/0ff5ceb7cbe3), 16 min (Video)
6. [An Overview of Linear Algebra](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/57f1139cba09), 50 min (Video)
7. [An Overview of Key Ideas](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/982c9ec4d6b0), 8 min (Video)
8. [Elimination with Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/b0ae1b4326a9), 48 min (Video)
9. [Recitation: Elimination with Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/6bc8c7ecb72d), 11 min (Video)
10. [Multiplication and Inverse Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/3720b4e95209), 47 min (Video)
11. [Inverse Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/3bb94640d322), 9 min (Video)
12. [Factorization into A = LU](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/104e14cef176), 49 min (Video)
13. [LU Decomposition](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/bc03473ba3f4), 10 min (Video)
14. [Transposes, Permutations, Vector Spaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/80d262b2b127), 48 min (Video)
15. [Subspaces of Three Dimensional Space](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/1f5bc0c7e971), 15 min (Video)
16. [三维空间的子空间](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/109e4482179f), 14 min (Video)
17. [Column Space and Nullspace](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/2ad36823965d), 47 min (Video)
18. [Vector Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/7bbe1e531a2e), 9 min (Video)
19. [Solving Ax = 0: Pivot Variables, Special Solutions](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/02bba7a6b600), 44 min (Video)
20. [Solving Ax=0](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/95aa73fdbe6a), 11 min (Video)
21. [Solving Ax = b: Row Reduced Form R](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/d5e2e6ed0212), 48 min (Video)
22. [Solving Ax=b](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/73a60480a57d), 10 min (Video)
23. [Independence, Basis and Dimension](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/7be3625f1b6f), 51 min (Video)
24. [Basis and Dimension](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/9f9a85b078e3), 9 min (Video)
25. [The Four Fundamental Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/a6d6eb36df9d), 50 min (Video)
26. [Computing the Four Fundamental Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/e84e70d8107e), 11 min (Video)
27. [Matrix Spaces; Rank 1; Small World Graphs](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/cb0b2613ccd5), 46 min (Video)
28. [Matrix Spaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/f8368b740c2e), 9 min (Video)
29. [Graphs, Networks, Incidence Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/3583f0aac4a5), 48 min (Video)
30. [Graphs and Networks](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/87de806a5c04), 13 min (Video)
31. [Exam 1 Review](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/7bbc5d966162), 48 min (Video)
32. [Exam 1 Problem Solving](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/6c3de7a6361c), 15 min (Video)
33. [Orthogonal Vectors and Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/bd3119298f4d), 50 min (Video)
34. [Problem Solving: Orthogonal Vectors and Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/964e1cf166de), 11 min (Video)
35. [Lecture 15: Projections onto Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/058bb1a682bc), 49 min (Video)
36. [Problem Solving: Projection onto Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/5451af3fdcd7), 10 min (Video)
37. [Lecture 16: Projection Matrices and Least Squares](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/0f1bc30fa32e), 49 min (Video)
38. [Problem Solving: Least Squares Approximation](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/935029a8d052), 9 min (Video)
39. [Lecture 17: Orthogonal Matrices and Gram-Schmidt](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/bc6988543769), 50 min (Video)
40. [Problem Solving: Gram-Schmidt Orthogonalization](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/bee9f67f0ca6), 10 min (Video)
41. [Lecture 18: Properties of Determinants](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/141affa3a5e3), 50 min (Video)
42. [Problem Solving: Properties of Determinants](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/fd729a5ba927), 10 min (Video)
43. [Lecture 19: Determinant Formulas and Cofactors](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/6eaf85320d46), 54 min (Video)
44. [Problem Solving: Determinants](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/99284cacf4cc), 13 min (Video)
45. [行列式](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/a338bc1e7d27), 13 min (Video)
46. [Lecture 20: Cramer's Rule, Inverse Matrix and Volume](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/5e370fb35812), 52 min (Video)
47. [Problem Solving: Determinants and Volume](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/1743cdbb99c0), 14 min (Video)
48. [行列式和体积](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/d33a9205dfe2), 12 min (Video)
49. [Lecture 21: Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/4c89a327ec9a), 52 min (Video)
50. [Problem Solving: Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/e0c0ef3b5436), 10 min (Video)
51. [Lecture 22: Diagonalization and Powers of A](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/d50c97bb88c3), 52 min (Video)
52. [Problem Solving: Powers of a Matrix](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/d5118136c753), 10 min (Video)
53. [Lecture 23: Differential Equations and exp(At)](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/ee6854dac5b5), 52 min (Video)
54. [Problem Solving: Differential Equations and exp(At)](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/7950e08ab4a8), 19 min (Video)
55. [微分方程指数矩阵(At)](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/1129705aa562), 15 min (Video)
56. [Lecture 24: Markov Matrices; Fourier Series](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/f27a8dad9b69), 52 min (Video)
57. [Problem Solving: Markov Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/01dbcfe33c6b), 12 min (Video)
58. [Exam 2 Review](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/5cd486550c17), 49 min (Video)
59. [Exam 2 Problem Solving](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/e6093f99a2bd), 18 min (Video)
60. [第二次考试例题](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/21e5efe24b5c), 19 min (Video)
61. [Lecture 25: Symmetric Matrices and Positive Definiteness](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/bdf94d0e3761), 44 min (Video)
62. [Problem Solving: Symmetric Matrices and Positive Definiteness](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/c0ca0b8c0e95), 13 min (Video)
63. [Lecture 26: Complex Matrices; Fast Fourier Transform (FFT)](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/f91d08350eaa), 48 min (Video)
64. [Problem Solving: Complex Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/59bf2de9b5c8), 14 min (Video)
65. [Lecture 27: Positive Definite Matrices and Minima](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/23899e372aff), 51 min (Video)
66. [Problem Solving: Positive Definite Matrices and Minima](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/3b833856d581), 13 min (Video)
67. [Lecture 28: Similar Matrices and Jordan Form](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/04d81cc1cc99), 46 min (Video)
68. [Problem Solving: Similar Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/5e0d94d9c891), 9 min (Video)
69. [Lecture 29: Singular Value Decomposition](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/2f5d4a1d50c6), 41 min (Video)
70. [Problem Solving: Computing the Singular Value Decomposition](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/f3bc98752f17), 12 min (Video)
71. [Lecture 30: Linear Transformations and their Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/016e10e420ee), 50 min (Video)
72. [Problem Solving: Linear Transformations](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/debc65c1e423), 11 min (Video)
73. [Lecture 31: Change of Basis; Image Compression](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/94e9cc4d20f9), 51 min (Video)
74. [Problem Solving: Change of Basis](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/06942b3dcc6d), 13 min (Video)
75. [Lecture 33: Left and Right Inverses; Pseudoinverse](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/91e9f46aa26f), 42 min (Video)
76. [Problem Solving: Pseudoinverses](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/f179db23ba2b), 15 min (Video)
77. [Exam 3 Review](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/7a443755ae07), 48 min (Video)
78. [Exam 3 Problem Solving](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/00934cdca243), 13 min (Video)
79. [Final Course Review](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/a91f91524762), 44 min (Video)
80. [Final Exam Problem Solving](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/192fd2737ce8), 13 min (Video)
81. [Gil Strang's Final 18.06 Linear Algebra Lecture](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/fd5cf1ea998d), 1 h 6 min (Video)
82. [The Geometry of Linear Equations](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/8f6b3ef5fa4c), 40 min (Video)
83. [Geometry of Linear Algebra](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/cb2858969e5d), 17 min (Video)
84. [线性代数的几何表示](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/7efc5869dcf2), 16 min (Video)
85. [An Overview of Linear Algebra](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/46a08aace8d1), 50 min (Video)
86. [An Overview of Key Ideas](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/7eb911350a13), 8 min (Video)
87. [Lecture: Elimination with Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/d26685f62e08), 48 min (Video)
88. [Elimination with Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/b5db2c9f9fa1), 11 min (Video)
89. [Multiplication and Inverse Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/a0b066d91e7b), 47 min (Video)
90. [Inverse Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/f52fadbb76e8), 9 min (Video)
91. [Factorization into A = LU](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/e53a0bc0fec9), 49 min (Video)
92. [LU Decomposition](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/6b5c2aad2bae), 10 min (Video)
93. [Transposes, Permutations, Vector Spaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/48825e3bcf69), 48 min (Video)
94. [Subspaces of Three Dimensional Space](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/2f4c4fb94dab), 15 min (Video)
95. [三维空间的子空间](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/456fcdceb105), 14 min (Video)
96. [Column Space and Nullspace](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/c11f06a5354d), 47 min (Video)
97. [Vector Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/1232e510e0e3), 9 min (Video)
98. [Solving Ax = 0: Pivot Variables, Special Solutions](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/0d6dde129834), 44 min (Video)
99. [Solving Ax=0](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/17e7d5ee9b0f), 11 min (Video)
100. [Solving Ax = b: Row Reduced Form R](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/546fc113caef), 48 min (Video)
101. [Solving Ax=b](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/0d38109a24f2), 10 min (Video)
102. [Independence, Basis and Dimension](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/b6de7bfe0654), 51 min (Video)
103. [Basis and Dimension](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/356fa34afa13), 9 min (Video)
104. [The Four Fundamental Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/3b1fbca64b14), 50 min (Video)
105. [Computing the Four Fundamental Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/d2dd51ba8183), 11 min (Video)
106. [Matrix Spaces; Rank 1; Small World Graphs](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/3003c7e1ff3a), 46 min (Video)
107. [Matrix Spaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/2b896c95f372), 9 min (Video)
108. [Graphs, Networks, Incidence Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/f7f8e489335a), 48 min (Video)
109. [Graphs and Networks](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/4146064c156a), 13 min (Video)
110. [Exam 1 Review](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/a4354d2cc928), 48 min (Video)
111. [Exam 1 Problem Solving](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/4b044e4626f1), 15 min (Video)
112. [Orthogonal Vectors and Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/c63fd79ac503), 50 min (Video)
113. [Problem Solving: Orthogonal Vectors and Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/f99b8a358ab6), 11 min (Video)
114. [Lecture 15: Projections onto Subspaces](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/8480b202ff51), 49 min (Video)
115. [Lecture 16: Projection Matrices and Least Squares](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/56014bdb0625), 49 min (Video)
116. [Problem Solving: Least Squares Approximation](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/069cee90e968), 9 min (Video)
117. [Lecture 17: Orthogonal Matrices and Gram-Schmidt](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/65bbc6902d93), 50 min (Video)
118. [Problem Solving: Gram-Schmidt Orthogonalization](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/085430a725ca), 10 min (Video)
119. [Lecture 18: Properties of Determinants](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/6575e4e63d9d), 50 min (Video)
120. [Problem Solving: Properties of Determinants](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/9e301318b541), 10 min (Video)
121. [Lecture 19: Determinant Formulas and Cofactors](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/1552776366dd), 54 min (Video)
122. [Problem Solving: Determinants](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/b9aeede102c4), 13 min (Video)
123. [行列式](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/491f29d065fa), 13 min (Video)
124. [Lecture 20: Cramer's Rule, Inverse Matrix and Volume](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/9652a0ec22bc), 52 min (Video)
125. [Problem Solving: Determinants and Volume](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/900088cc443e), 14 min (Video)
126. [行列式和体积](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/882024d7faf8), 12 min (Video)
127. [Lecture 21: Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/4e0b21207f6a), 52 min (Video)
128. [Problem Solving: Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/685ae278f390), 10 min (Video)
129. [Lecture 22: Diagonalization and Powers of A](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/0e0c95170167), 52 min (Video)
130. [Problem Solving: Powers of a Matrix](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/d7ce96739b2a), 10 min (Video)
131. [Lecture 23: Differential Equations and exp(At)](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/5e79cae5bda5), 52 min (Video)
132. [Problem Solving: Determinants and VolumeDifferential Equations and exp(At)](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/fba338370186), 19 min (Video)
133. [微分方程指数矩阵(At)](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/e98abe7f66d6), 15 min (Video)
134. [Lecture 24: Markov Matrices; Fourier Series](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/9f7c048886eb), 52 min (Video)
135. [Problem Solving: Markov Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/13dc8f4c5bb6), 12 min (Video)
136. [Exam 2 Review](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/970a50412517), 49 min (Video)
137. [Exam 2 Problem Solving](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/5e2cefadeb12), 18 min (Video)
138. [第二次考试例题](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/c10cba7c6371), 19 min (Video)
139. [Lecture 25: Symmetric Matrices and Positive Definiteness](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/bf7c49fc4111), 44 min (Video)
140. [Problem Solving: Symmetric Matrices and Positive Definiteness](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/78f2c6308c93), 13 min (Video)
141. [Lecture 26: Complex Matrices; Fast Fourier Transform (FFT)](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/15adbc03d0e7), 48 min (Video)
142. [Problem Solving: Complex Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/5f5ebe3eee39), 14 min (Video)
143. [Lecture 27: Positive Definite Matrices and Minima](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/dd0f692782d8), 51 min (Video)
144. [Problem Solving: Positive Definite Matrices and Minima](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/b8bfa4131f58), 13 min (Video)
145. [Lecture 28: Similar Matrices and Jordan Form](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/0f18be938f60), 46 min (Video)
146. [Problem Solving: Similar Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/86e9fad621af), 9 min (Video)
147. [Lecture 29: Singular Value Decomposition](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/e549d29470a2), 41 min (Video)
148. [Problem Solving: Determinants and VolumeComputing the Singular Value Decomposition](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/74d3c7393daf), 12 min (Video)
149. [Lecture 30: Linear Transformations and their Matrices](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/eb949dfb17bd), 50 min (Video)
150. [Problem Solving: Linear Transformations](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/59bb1de8c496), 11 min (Video)
151. [Lecture 31: Change of Basis; Image Compression](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/e8b6b69da0d1), 51 min (Video)
152. [Problem Solving: Change of Basis](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/05ffd074c91c), 13 min (Video)
153. [Lecture 33: Left and Right Inverses; Pseudoinverse](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/9d791b8164eb), 42 min (Video)
154. [Problem Solving: Pseudoinverses](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/25bb9151a325), 15 min (Video)
155. [Exam 3 Review](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/34a7c7e2e385), 48 min (Video)
156. [Exam 3 Problem Solving](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/2a6342f32ceb), 13 min (Video)
157. [Final Course Review](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/55496aa6bbfa), 44 min (Video)
158. [Final Exam Problem Solving](https://invisiblenetwork.ai/learn/mit/18-06sc-linear-algebra-fall-2011/957850ebb64a), 13 min (Video)