• Sections 5 and 7 were lectured on the same day (Tuesday) and the contents for these two sections have significant overlap. The lectures in the later section -- Section 7 -- are slightly refined and faster.
• Section 6 was lectured on a different day (Thursday).
• Naming convention:
  • mmdd_S#: Month + Date + Section No. (5 or 6 or 7)
    • This is the entire record for the whole 75 minutes lecture, which are usually cut into short pieces:
    • mmdd_S#-i: i refers to the ith part.
• Back to the Course Page.

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1. 0820_S6-1 Course policies and general introduction
2. 0820_S6-2 Section 1-1 Solutions and elementary operations
3. 0820_S6-3 Answer some questions on the chat
4. 0820_S6
5. 0825_S5-1 General discussion
6. 0825_S5-2 Section 1-2 Gaussian elimination
7. 0825_S5-3 Section 1-3 Homogeneous equations
8. 0825_S5
9. 0825_S7-1 General discussion
10. 0825_S7-2 Section 1-2 Gaussian elimination
11. 0825_S7-3 Section 1-3 Homogeneous equations
12. 0825_S7
13. 0826_Reduced_Echolon_Form-1 General discussion
14. 0826_Reduced_Echolon_Form
15. 0827_S6-1 General opening of the class
16. 0827_S6-2 Section 2-1 Matrix addition
17. 0827_S6-3 Section 2-2 Matrix-vector multiplication -- part 1
18. 0827_S6
19. 0901_S5-1 General discussion
20. 0901_S5-2 Section 2-2 Matrix-vector multiplication -- part 2
21. 0901_S5-3 Section 2-3 Matrix multiplication
22. 0901_S5
23. 0901_S7-1 General discussion
24. 0901_S7-2 Section 2-2 Matrix-vector multiplication -- part 2
25. 0901_S7-3 Section 2-3 Matrix multiplication
26. 0901_S7
27. 0903_Officehour-1 Still another quiz problem B1 36
28. 0903_Officehour-2 Still another quiz problem B1 51
29. 0903_Officehour-3 HW 2-2-9
30. 0903_Officehour-4 HW 2-2-14
31. 0903_Officehour
32. 0903_S7-1 General opening of the class
33. 0903_S7-2 One quiz problem for unique solution B1 41
34. 0903_S7-3 Explain the rank
35. 0903_S7-4 HW 2-3-17
36. 0903_S7-5 Another quiz problem B2 44
37. 0903_S7-6 HW 2-3-34
38. 0903_S7-7 HW 2-3-13-d
39. 0903_S7-8 HW 2-3-13-f
40. 0903_S7
41. 0908_S5-1 General opening
42. 0908_S5-2 Section 1-1 Matrix inverses
43. 0908_S5
44. 0908_S7-1 General opening
45. 0908_S7-2 Section 1-1 Matrix inverses
46. 0908_S7
47. 0910_S6-1 General opening
48. 0910_S6-2 Section 2-5 Elementary matrices
49. 0910_S6-3 Section 2-7 The LU factorization - part I
50. 0910_S6
51. 0915_One_Example_LU_Decomposition
52. 0915_S5-1 General opening
53. 0915_S5-2 Section 2-6 Linear transformations
54. 0915_S5-3 Section 2-7 The LU factorization - part II
55. 0915_S5
56. 0915_S7-1 General opening
57. 0915_S7-2 Section 2-6 Linear transformations
58. 0915_S7-3 Section 2-7 The LU factorization - part II
59. 0915_S7
60. 0917_S6-1 General opening
61. 0917_S6-2 Section 3-1 Cofactor Expansion
62. 0917_S6-3 Section 3-2 Determinants and Matrix Inverses - part I
63. 0917_S6
64. 0922_officehour_HW 3-1-22
65. 0922_S5-1 General opening
66. 0922_S5-2 Section 3-1 Cofactor Expansion -- diagram for 4x4
67. 0922_S5-3 Section 3-2 Determinants and Matrix Inverses - part I
68. 0922_S5-4 Section 3-3 Determinants and Eigenvalues - part I
69. 0922_S5
70. 0922_S7-1 General opening
71. 0922_S7-2 Section 3-1 Cofactor Expansion -- diagram for 4x4
72. 0922_S7-3 Section 3-2 Determinants and Matrix Inverses - part I
73. 0922_S7-4 Section 3-3 Determinants and Eigenvalues - part I
74. 0922_S7
75. 0924_S6-1 General opening
76. 0924_S6-2 Comments on Vandermonde determinant
77. 0924_S6-3 Section 3-3 Determinants and Eigenvalues - part II
78. 0924_S6-4 Section 3-3 Determinants and Eigenvalues - part III
79. 0924_S6-5 Section 3-3 Determinants and Eigenvalues - part IV
80. 0924_S6
81. 0929_S5-1 Exercise 3-3-22 P
82. 0929_S5-1 General opening
83. 0929_S5-2 Exercise 3-1-17 H
84. 0929_S5-2 Exercise 3-3-20 P(1)
85. 0929_S5-2 Exercise 3-3-20 P
86. 0929_S5-3 Exercise 3-2-32 P
87. 0929_S5-4 Exercise 3-2-34 P
88. 0929_S5-5 Exercise 3-3-22 P
89. 0929_S5-6 Exercise 3-3-20 P
90. 0929_S5
91. 0929_S7-10 Exercise 3-1-22 P
92. 0929_S7-1 General opening
93. 0929_S7-2 Exercise 3-3-7 H
94. 0929_S7-3 Exercise 3-1-18 H
95. 0929_S7-4 Exercise 3-1-6 H
96. 0929_S7-5 Exercise 3-1-20 P
97. 0929_S7-6 Exercise 3-2-30 P
98. 0929_S7-7 Exercise 3-3-22 P
99. 0929_S7-8 Exercise 3-3-25 P
100. 0929_S7-9 Exercise 3-3-30 P
101. 0929_S7
102. 1001_Officehour-1 Problem from Phase I -- 122
103. 1001_Officehour-2 Exercise 3-3-24 H
104. 1001_Officehour
105. 1001_S6-1 General opening
106. 1001_S6-2 Problem from Phase I -- 112
107. 1001_S6-3 Problem from Phase I -- 99
108. 1001_S6-4 Problem from Phase I -- 38
109. 1001_S6-5 Problem from Phase I -- 118
110. 1001_S6-6 Problem from Phase I -- 116
111. 1001_S6-7 Ending words
112. 1001_S6
113. 1006_S5-1 General opening
114. 1006_S5-2 Section 4-1 Vector and Lines -- short version
115. 1006_S5-3 Section 4-1 Vector and Lines -- extended version
116. 1006_S5-4 Ending words
117. 1006_S5
118. 1006_S7-1 General opening
119. 1006_S7-2 Section 4-1 Vector and Lines -- short version
120. 1006_S7-3 Section 4-1 Vector and Lines -- extended version
121. 1006_S7-4 Ending remarks
122. 1006_S7
123. 1008_S6-1 General opening
124. 1008_S6-2 Section 4-2 Projections and Plains -- Dot Product
125. 1008_S6-3 Section 4-2 Projections and Plains -- Projection
126. 1008_S6-4 Section 4-2 Projections and Plains -- Plain Equation
127. 1008_S6-5 Section 4-2 Projections and Plains -- Cross Product
128. 1008_S6
129. 1012_Officehour-1 Section 4-4 -- Question and Answer
130. 1012_Officehour
131. 1013_Officehour-1 Sample Problem from Phase I of HW8 -- 139
132. 1013_Officehour-2 Sample Problem from Phase I of HW8 -- 12
133. 1013_Officehour-3 Exercise 4.4.1-a
134. 1013_Officehour-4 Sample Problem from Phase I of HW8 -- 76
135. 1013_Officehour-5 Sample Problem from Phase I of HW8 -- 21
136. 1013_Officehour
137. 1013_S5-1 General opening
138. 1013_S5-2 Section 4-2 Projections and Plains -- Shortest distance
139. 1013_S5-3 Section 5-1 Subspace and spanning -- Definition and Examples
140. 1013_S5-4 Section 5-1 Subspace and spanning -- Null Space and Image Space
141. 1013_S5-5 Section 5-1 Subspace and spanning -- Eigenspace
142. 1013_S5-6 Section 5-1 Subspace and spanning -- Linear Combinations and Spanning
143. 1013_S5
144. 1013_S7-1 General opening
145. 1013_S7-2 Section 5-1 Subspace and spanning -- Definition and Examples
146. 1013_S7-3 Section 5-1 Subspace and spanning -- Null Space and Image Space
147. 1013_S7-4 Section 5-1 Subspace and spanning -- Eigenspace
148. 1013_S7-5 Section 5-1 Subspace and spanning -- Linear Combinations and Spanning
149. 1013_S7
150. 1015_Officehour-1 Sample Problem from Phase I of HW8 -- 142
151. 1015_Officehour
152. 1015_S6-1 General opening
153. 1015_S6_2-1 Section 5-2 Independence and Dimension -- Properties of Basis
154. 1015_S6_2
155. 1015_S6-2 Section 5-2 Independence and Dimension -- Definition of Independence
156. 1015_S6-3 Section 5-2 Independence and Dimension -- Examples of Independent Vectors
157. 1015_S6-4 Section 5-2 Independence and Dimension -- Unique Representation Theorem
158. 1015_S6-5 Section 5-2 Independence and Dimension -- Two Geometric Example
159. 1015_S6-6 Section 5-2 Independence and Dimension -- Independence and Spanning
160. 1015_S6-7 Section 5-2 Independence and Dimension -- Bases and Dimensions
161. 1015_S6
162. 1019_Officehour-1 A question on the lecture slides
163. 1019_Officehour-2 Lab question: Ex 5-1-7
164. 1019_Officehour-3 Lab question: Ex 5-1-13
165. 1019_Officehour
166. 1020_Officehour-1 Bank 5-73
167. 1020_Officehour-2 Bank 5-64
168. 1020_Officehour-3 A question on the lecture slides
169. 1020_Officehour
170. 1020_S5-1 General opening
171. 1020_S5-2 Section 5-3 Orthogonality -- Dot Products
172. 1020_S5-3 Section 5-3 Orthogonality -- Cauchy-Schwartz Inequality
173. 1020_S5-4 Section 5-3 Orthogonality -- Orthogonality
174. 1020_S5-5 Section 5-3 Orthogonality -- Orthogonal Set and Independent Set
175. 1020_S5-6 Section 5-3 Orthogonality -- Fourier Expansions
176. 1020_S5-7 Bank 5-29
177. 1020_S5
178. 1020_S7-1 General opening
179. 1020_S7-2 Section 5-3 Orthogonality -- Dot Products
180. 1020_S7-3 Section 5-3 Orthogonality -- Cauchy-Schwartz Inequality
181. 1020_S7-4 Section 5-3 Orthogonality -- Orthogonality
182. 1020_S7-5 Section 5-3 Orthogonality -- Orthogonal Set and Independent Set
183. 1020_S7-6 Section 5-3 Orthogonality -- Fourier Expansions
184. 1020_S7-7 Section 5-3 Orthogonality -- Bank 5-43
185. 1020_S7-8 Section 5-3 Orthogonality -- Bank 5-29
186. 1020_S7
187. 1022_S6-1 General opening
188. 1022_S6-2 Section 5-4 Rank of a Matrix -- Row Spaces and Column Spaces
189. 1022_S6-3 Section 5-4 Rank of a Matrix -- Rank Theorem
190. 1022_S6-4 Section 5-4 Rank of a Matrix -- Rank-Nullity Theorem
191. 1022_S6-5 Section 5-4 Rank of a Matrix -- Full Rank Case
192. 1022_S6-6 Section 5-4 Rank of a Matrix -- Post words
193. 1022_S6
194. 1023_Officehour-1 Bank 5-27 -- Complete Discussion
195. 1023_Officehour-2 Bank 5-27 -- Concise Version
196. 1023_Officehour-3 Bank 5-37
197. 1023_Officehour-4 Bank 5-43
198. 1023_Officehour
199. 1027_officehour-1 Practice Problem -- Ex 5-3-16 H
200. 1027_officehour-2 Bank 5-9
201. 1027_officehour-3 Bank 5-32
202. 1027_officehour-4 Practice Problem -- Ex 5-4-13 H
203. 1027_officehour-5 Bank 5-68
204. 1027_officehour
205. 1027_S5-1 General opening
206. 1027_S5-2 Section 5-5 Similarity and Diagonalization -- Similar Matrices
207. 1027_S5-3 Section 5-5 Similarity and Diagonalization -- Diagonalization Revisited
208. 1027_S5-4 Section 5-5 Similarity and Diagonalization -- Algebraic and Geometric Multiplicities
209. 1027_S5-5 Section 5-5 Similarity and Diagonalization -- Characterizing Diagonalization
210. 1027_S5-6 Section 5-5 Similarity and Diagonalization -- Complex Eigenvalues and Real and Symmetric Matrices
211. 1027_S5-7 Section 5-5 Similarity and Diagonalization -- Post words
212. 1027_S5
213. 1027_S7-10 Practice Problem -- Ex 5-5-7 P
214. 1027_S7-11 Practice Problem -- Ex 5-5-10 P
215. 1027_S7-12 Practice Problem -- Ex 5-5-17 P
216. 1027_S7-1 General Opening
217. 1027_S7-2 Practice Problem -- Ex 5-1-7 L
218. 1027_S7-3 Practice Problem -- Ex 5-1-14 H
219. 1027_S7-4 Practice Problem -- Ex 5-1-18 P
220. 1027_S7-5 Practice Problem -- Ex 5-4-5 H
221. 1027_S7-6 Practice Problem -- Ex 5-4-8 L
222. 1027_S7-7 Practice Problem -- Ex 5-4-10 L
223. 1027_S7-8 Practice Problem -- Ex 5-4-18 P
224. 1027_S7-9 Practice Problem -- Ex 5-5-3 P
225. 1027_S7
226. 1028_officehour-1 Bank 5-93
227. 1028_officehour-2 Bank 4-37
228. 1028_officehour-3 Bank 5-48
229. 1028_officehour
230. 1029_S6-10 A Question on basis
231. 1029_S6-11 Practice Problem -- Ex 5-5-7 P -- Revisited
232. 1029_S6-1 A Question Regarding Parenthesis
233. 1029_S6-2 General Opening
234. 1029_S6-3 Practice Problem -- Ex 5-5-18 P
235. 1029_S6-4 Practice Problem -- Ex 5-5-12 P
236. 1029_S6-5 Practice Problem -- Ex 5-4-11 P Merged
237. 1029_S6-5 Practice Problem -- Ex 5-4-11 P
238. 1029_S6-6 Practice Problem -- Ex 5-4-3
239. 1029_S6-7 Orthogonal Eigenvectors
240. 1029_S6-8 A Question on Independent Eigenvectors
241. 1029_S6-9 Practice Problem -- Ex 5-4-11 Merged
242. 1029_S6-9 Practice Problem -- Ex 5-4-11 Revisited
243. 1029_S6
244. 1103_S5-1 General Opening
245. 1103_S5-2 Section 6-1 Examples and Basic Properties -- Definition of Vector Spaces
246. 1103_S5-3 Section 6-1 Examples and Basic Properties -- Matrices
247. 1103_S5-4 Section 6-1 Examples and Basic Properties -- Polynomials
248. 1103_S5-5 Section 6-1 Examples and Basic Properties -- More Examples
249. 1103_S5-6 Section 6-2 Subspaces and Spanning Sets -- Subspaces
250. 1103_S5-7 Section 6-2 Subspaces and Spanning Sets -- Spanning Sets
251. 1103_S5
252. 1103_S7-1 General Opening
253. 1103_S7-2 Quick reviewing of Section 6-1
254. 1103_S7-3 Quick reviewing of Section 6-2
255. 1103_S7-4 Section 6-3 Linear independence and Dimension -- Linearly Independent
256. 1103_S7-5 Section 6-3 Linear independence and Dimension -- Fundamental Theorem
257. 1103_S7-6 Section 6-3 Linear independence and Dimension -- Basis and Dimensions
258. 1103_S7
259. 1106_S6-1 Section 6-4 Finite Dimensional Spaces -- Structure
260. 1106_S6-2 Section 6-4 Finite Dimensional Spaces -- Generalizing from Rn
261. 1106_S6-3 Section 6-4 Finite Dimensional Spaces -- Form a Basis by Deleting Vectors
262. 1106_S6-4 Section 6-4 Finite Dimensional Spaces -- Subspaces
263. 1106_S6-5 Section 6-4 Finite Dimensional Spaces -- Form a Basis by Adding Vectors
264. 1106_S6-6 Section 6-4 Finite Dimensional Spaces -- Sums and Intersections
265. 1106_S6
266. 1110_S5-1 General Opening and Structure of Section 8-1
267. 1110_S5-2 Section 8-1 Orthogonal Complements and Projections -- Orthogonal Basis
268. 1110_S5-3 Section 8-1 Orthogonal Complements and Projections -- Orthogonal Complements
269. 1110_S5-4 Section 8-1 Orthogonal Complements and Projections -- Projection Theorem
270. 1110_S5-5 Section 8-1 Orthogonal Complements and Projections -- Projection as a Linear Transformation
271. 1110_S5
272. 1110_S7-1 General Opening
273. 1110_S7-2 Quick reviewing of Section 8-1
274. 1110_S7-3 Section 8-2 Orthogonal Diagonalization -- Orthogonal Matrices
275. 1110_S7-4 Section 8-2 Orthogonal Diagonalization -- Principal Axes Theorem
276. 1110_S7-5 Section 8-2 Orthogonal Diagonalization -- One Example of Orthogonal Diagonalization by heart
277. 1110_S7-6 Section 8-2 Orthogonal Diagonalization -- Quadratic Forms
278. 1110_S7-7 Section 8-2 Orthogonal Diagonalization -- Schur Decomposition or Triangular Theorem
279. 1110_S7
280. 1112_S6-1 Some announcements before class
281. 1112_S6-2 Section 8-3 Positive Definite Matrices -- Definition and Properties
282. 1112_S6-3 Section 8-3 Positive Definite Matrices -- Cholesky Decomposition
283. 1112_S6-4 Section 8-4 QR Factorization -- Definition
284. 1112_S6-5 Section 8-4 QR Factorization -- Algorithm
285. 1112_S6-6 Final words -- Course Evaluation
286. 1112_S6
287. 1117_S5-1 Some announcements before class
288. 1117_S5-2 Section 8-6 Singular Value Decomposition -- Definition
289. 1117_S5-3 Section 8-6 Singular Value Decomposition -- Computations
290. 1117_S5-4 Section 8-6 Singular Value Decomposition -- Fundamental Subspaces
291. 1117_S5-5 Section 8-6 Singular Value Decomposition -- Application -- Polar Decomposition
292. 1117_S5-6 Section 8-6 Singular Value Decomposition -- Application -- Generalized Inverses
293. 1117_S5-7 Section 8-6 Singular Value Decomposition -- Application -- Linear Transformation
294. 1117_S5-8 Section 8-6 Singular Value Decomposition -- Application -- Image Compression
295. 1117_S5
296. 1117_S7-1 Some announcements before class
297. 1117_S7-2 Section 8-6 Singular Value Decomposition -- Definition
298. 1117_S7-3 Section 8-6 Singular Value Decomposition -- Computations
299. 1117_S7-4 Section 8-6 Singular Value Decomposition -- Fundamental Subspaces
300. 1117_S7-5 Section 8-6 Singular Value Decomposition -- Application -- Polar Decomposition
301. 1117_S7-6 Section 8-6 Singular Value Decomposition -- Application -- Generalized Inverses
302. 1117_S7-7 Section 8-6 Singular Value Decomposition -- Application -- Linear Transformation
303. 1117_S7-8 Section 8-6 Singular Value Decomposition -- Application -- Image Compression
304. 1117_S7-9 Post words
305. 1117_S7
306. 1119_S6-1 One conceptual problem from Chapter 6
307. 1119_S6-2 One problem related to orthogonal complement
308. 1119_S6-3 One problem for orthogonal diagonalizing quadratic form
309. 1119_S6-4 One problem for abstract vector spaces
310. 1119_S6
311. 1124_S5-1 Bank 8-31
312. 1124_S5-2 Bank 7-35
313. 1124_S5-3 Bank 6-52
314. 1124_S5-4 One problem for polynomial diagonalization
315. 1124_S5-5 Post words
316. 1124_S5
317. 1124_S7-1 Batch of questions
318. 1124_S7-2 Bank 7-10
319. 1124_S7-3 A randomly generated problem by students solved with the help of computer
320. 1124_S7-4 A randomly generated problem by students for polynomial diagonalization
321. 1124_S7-5 Post words
322. 1124_S7