14. Positive Definite and Semidefinite Matrices - 1
1年前 1408观看
艾伦·爱德曼和茱莉亚
大学课程 / 外语
https://ocw.mit.edu/18-065S18 MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Professor Strang describes the four topics of the course: Linear Algebra, Deep Learning, Optimization, and Statistics.
共102集 10.8万人观看
1Course Introduction of 18.065 by Professor Strang07:03
2The Column Space of A Contains All Vectors Ax - 117:27- 3The Column Space of A Contains All Vectors Ax - 217:28
- 4The Column Space of A Contains All Vectors Ax - 317:23
5Multiplying and Factoring Matrices - 116:11- 6Multiplying and Factoring Matrices - 216:14
- 7Multiplying and Factoring Matrices - 316:03
8Orthonormal Columns in Q Give Q'Q = I - 116:31- 9Orthonormal Columns in Q Give Q'Q = I - 216:38
- 10Orthonormal Columns in Q Give Q'Q = I - 316:28
11Eigenvalues and Eigenvectors - 116:21- 12Eigenvalues and Eigenvectors - 216:22
- 13Eigenvalues and Eigenvectors - 316:21
14Positive Definite and Semidefinite Matrices - 115:12- 15Positive Definite and Semidefinite Matrices - 215:19
- 16Positive Definite and Semidefinite Matrices - 315:03
17Singular Value Decomposition (SVD) - 117:54- 18Singular Value Decomposition (SVD) - 217:59
- 19Singular Value Decomposition (SVD) - 317:51
20Eckart-Young - The Closest Rank k Matrix to A - 115:48- 21Eckart-Young - The Closest Rank k Matrix to A - 215:49
- 22Eckart-Young - The Closest Rank k Matrix to A - 315:46
23Norms of Vectors and Matrices - 116:30- 24Norms of Vectors and Matrices - 216:30
- 25Norms of Vectors and Matrices - 316:26
26Four Ways to Solve Least Squares Problems - 116:40- 27Four Ways to Solve Least Squares Problems - 216:41
- 28Four Ways to Solve Least Squares Problems - 316:32
29Survey of Difficulties with Ax = b - 116:35- 30Survey of Difficulties with Ax = b - 216:39
- 31Survey of Difficulties with Ax = b - 316:27
32Minimizing _x_ Subject to Ax = b - 116:50- 33Minimizing _x_ Subject to Ax = b - 216:52
- 34Minimizing _x_ Subject to Ax = b - 316:46
35Computing Eigenvalues and Singular Values - 116:32- 36Computing Eigenvalues and Singular Values - 216:38
- 37Computing Eigenvalues and Singular Values - 316:29
38Randomized Matrix Multiplication - 117:31- 39Randomized Matrix Multiplication - 217:36
- 40Randomized Matrix Multiplication - 317:29
41Low Rank Changes in A and Its Inverse - 116:54- 42Low Rank Changes in A and Its Inverse - 216:55
- 43Low Rank Changes in A and Its Inverse - 316:49
44Matrices A(t) Depending on t, Derivative = dA_dt - 117:00- 45Matrices A(t) Depending on t, Derivative = dA_dt - 217:01
- 46Matrices A(t) Depending on t, Derivative = dA_dt - 316:54
47Derivatives of Inverse and Singular Values - 114:25- 48Derivatives of Inverse and Singular Values - 214:32
- 49Derivatives of Inverse and Singular Values - 314:25
50Rapidly Decreasing Singular Values - 116:54- 51Rapidly Decreasing Singular Values - 216:56
- 52Rapidly Decreasing Singular Values - 316:52
53Counting Parameters in SVD, LU, QR, Saddle Points - 116:23- 54Counting Parameters in SVD, LU, QR, Saddle Points - 216:24
- 55Counting Parameters in SVD, LU, QR, Saddle Points - 316:16
56Saddle Points Continued, Maxmin Principle - 117:27- 57Saddle Points Continued, Maxmin Principle - 217:32
- 58Saddle Points Continued, Maxmin Principle - 317:27
59Definitions and Inequalities - 118:23- 60Definitions and Inequalities - 218:30
- 61Definitions and Inequalities - 318:19
62Minimizing a Function Step by Step - 117:57- 63Minimizing a Function Step by Step - 218:02
- 64Minimizing a Function Step by Step - 317:50
65Gradient Descent - Downhill to a Minimum - 117:37- 66Gradient Descent - Downhill to a Minimum - 217:39
- 67Gradient Descent - Downhill to a Minimum - 317:36
68Accelerating Gradient Descent (Use Momentum) - 116:23- 69Accelerating Gradient Descent (Use Momentum) - 216:23
- 70Accelerating Gradient Descent (Use Momentum) - 316:23
71Linear Programming and Two-Person Games - 117:54- 72Linear Programming and Two-Person Games - 218:00
- 73Linear Programming and Two-Person Games - 317:52
74Stochastic Gradient Descent - 117:43- 75Stochastic Gradient Descent - 217:49
- 76Stochastic Gradient Descent - 317:37
77Structure of Neural Nets for Deep Learning - 117:48- 78Structure of Neural Nets for Deep Learning - 217:54
- 79Structure of Neural Nets for Deep Learning - 317:47
80Backpropagation - Find Partial Derivatives - 117:35- 81Backpropagation - Find Partial Derivatives - 217:35
- 82Backpropagation - Find Partial Derivatives - 317:36
83Completing a Rank-One Matrix, Circulants! - 116:40- 84Completing a Rank-One Matrix, Circulants! - 216:44
- 85Completing a Rank-One Matrix, Circulants! - 316:34
86Eigenvectors of Circulant Matrices - Fourier Matrix - 117:35- 87Eigenvectors of Circulant Matrices - Fourier Matrix - 217:36
- 88Eigenvectors of Circulant Matrices - Fourier Matrix - 317:28
89ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule - 115:49- 90ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule - 215:50
- 91ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule - 315:43
92Neural Nets and the Learning Function - 118:45- 93Neural Nets and the Learning Function - 218:48
- 94Neural Nets and the Learning Function - 318:44
95Distance Matrices, Procrustes Problem - 114:40- 96Distance Matrices, Procrustes Problem - 314:37
97Finding Clusters in Graphs - 111:39- 98Finding Clusters in Graphs - 211:40
- 99Finding Clusters in Graphs - 311:35
100Alan Edelman and Julia Language - 112:46- 101Alan Edelman and Julia Language - 212:50
- 102Alan Edelman and Julia Language - 312:45
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