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00:00
1.
Review of Matrix Theory and Multivariate Statistics
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00:57
2.
Basic Matrix Theory
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01:39
3.
Vector (向量) and Matrix(矩陣)
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03:19
4.
Important Matrices
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08:45
5.
Matrix Operation (運算)
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09:54
6.
Multiplication
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13:59
7.
Determinant (行列式值)
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19:25
8.
Inverse Matrix (反(逆)矩陣)
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24:51
9.
Find the Inverse Matrix for a 3×3 Matrix
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27:14
10.
Linearly Independent (線性獨立)
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27:15
11.
Find the Inverse Matrix for a 3×3 Matrix
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33:57
12.
Linearly Independent (線性獨立)
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38:30
13.
Rank (秩)
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42:46
14.
Positive (Negative) Definite Matrix (正定義)
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48:49
15.
Some Useful Formula
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51:23
16.
Latent (Characteristic) Root
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57:55
17.
An Example of Eigen Value (1)
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1:00:36
18.
An Example of Eigen Value (2)
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1:03:57
19.
An Example of Eigen Value (3)
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1:05:30
20.
Properties of Eigen Value
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1:09:11
21.
Derivative of matrix
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1:12:53
22.
Derivative of Matrix
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1:13:01
23.
Derivative of matrix
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1:13:07
24.
Derivative of Matrix
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1:18:02
25.
Multivariate Statistics
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1:18:06
26.
Multivariate Statistics
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1:18:17
27.
Expected Value and Variance of a Random Vector
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1:21:27
28.
2 Random Variable Case
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1:25:35
29.
Multivariate Normal Distribution
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1:29:15
30.
Proof of Y=𝐶𝑋+𝐵, Y~N(C𝜇+B, CΣC′),
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1:31:01
31.
Standard Normal Distribution
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1:31:03
32.
Proof of Y=𝐶𝑋+𝐵, Y~N(C𝜇+B, CΣC′),
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1:34:05
33.
Standard Normal Distribution
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1:37:38
34.
Function of Normal Distribution RV
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1:40:02
35.
An Example of Testing the Mean
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1:42:13
36.
An Example of Testing the Mean
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1:46:55
37.
What If 𝜎 2 Is Unknown
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1:49:47
38.
What If We Need to Test Two Hypotheses Jointly?
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1:54:04
39.
Chi-Square Distribution from Normal Distribution
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1:54:56
40.
What If We Need to Test Two Hypotheses Jointly?
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1:55:00
41.
Chi-Square Distribution from Normal Distribution
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1:55:26
42.
What If We Need to Test Two Hypotheses Jointly?
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1:55:44
43.
Chi-Square Distribution from Normal Distribution