#### 特征值分解

$A = Q\Lambda Q^T \tag{1.2}$

#### 奇异值分解

This shows how to decompose the matrix A into the product of three matrices: V describes an orthonormal basis in the domain, and U describes an orthonormal basis in the co-domain, and Σ describes how much the vectors in V are stretched to give the vectors in U.

#### 举个栗子3

Hole Par Phil Tiger Vijay
1 4 4 4 4
2 5 5 5 5
3 3 3 3 3
4 4 4 4 4
5 4 4 4 4
6 4 4 4 4
7 4 4 4 4
8 3 3 3 3
9 5 5 5 5

Phil Tiger Vijay
4 4 4
5 5 5
3 3 3
4 4 4
4 4 4
4 4 4
4 4 4
3 3 3
5 5 5
=
HoleDifficulty
4
5
3
4
4
4
4
3
5
$\times$
PlayerAbility
Phil Tiger Vijay
1 1 1

Phil Tiger Vijay
4 4 4
5 5 5
3 3 3
4 4 4
4 4 4
4 4 4
4 4 4
3 3 3
5 5 5
$=$
HoleDifficulty
0.33
0.41
0.25
0.33
0.33
0.33
0.33
0.25
0.41
$\times$
ScaleFactor
21.07
$\times$
PlayerAbility
Phil Tiger Vijay
0.58 0.58 0.58

#### 继续挖这个栗子

SVD分解就是利用隐藏的 feature 建立起矩阵行和列之间的联系。

Phil Tiger Vijay
4 4 5
4 5 5
3 3 2
4 5 4
4 4 4
3 5 4
4 4 3
2 4 4
5 5 5
$=$
HoleDifficulty 1-3
4.34 -0.18 -0.90
4.69 -0.38 -0.15
2.66 0.80 0.40
4.36 0.15 0.47
4.00 0.35 -0.29
4.05 -0.67 0.68
3.66 0.89 0.33
3.39 -1.29 0.14
5.00 0.44 -0.36
$\times$
PlayerAbility 1-3
Phil Tiger Vijay
0.91 1.07 1.00
0.82 -0.20 -0.53
-0.21 0.76 -0.62

Phil Tiger Vijay
4 4 5
4 5 5
3 3 2
4 5 4
4 4 4
3 5 4
4 4 3
2 4 4
5 5 5
$=$
HoleDifficulty 1-3
0.35 0.09 -0.64
0.38 0.19 -0.10
0.22 -0.40 0.28
0.36 -0.08 0.33
0.33 -0.18 -0.20
0.33 0.33 0.48
0.30 -0.44 0.23
0.28 0.64 0.10
0.41 -0.22 -0.25
$\times$
 ScaleFactor 1-3 21.07 0 0 0 2.01 0 0 0 1.42
$\times$
 PlayerAbility 1-3 Phil Tiger Vijay 0.53 0.62 0.58 -0.82 0.20 0.53 -0.21 0.76 -0.62

#### 后记

Markdown排版表格是件麻烦事，google了一下，发现个在线网站，可以很方便生成 $\LaTeX$ 和 Markdown 表格，安利下这个 神器~