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# System prepended metadata

title: Untitled

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`chapter04.tex`

L87:

Camera poses can construct the special orthogonal group $SO(3)$ and special euclidean group $SE(3)$ defined as follows: 
define 前面不用加逗號

L99:

However, $SO(3)$ does not have closure property under addition, which means that the addition of two rotation matrices is not a rotation matrix.
which 前面加逗號

L105-111:

可以提一下 $t$ 是甚麼

這裡的各個是式子比較沒有那麼重要，是不是可以用

```
\begin{align}
& R(t) R(t)^{T} = I.
\implies & \dot{R}(t) R(t)^{T} + R(t) \dot{R}(t)^{T} = 0.
\implies & \dot{R}(t) R(t)^{T} = -\bigg(\dot{R}(t) R(t)^{T}\bigg)^{T}.
\end{align}
```

另外 $\dot{R}(t)$ 是指對這個矩陣作微分嗎，沒看過這種 notation @@

L137:

可以提一下 $J_l$ 跟 $J_r$ 的物理意義，不然不知道這兩個函數怎麼跑出來的

有些 ^ 符號是甚麼意思，例如
![](https://i.imgur.com/bkPHwOS.png)
![](https://i.imgur.com/Z6Ob64y.png)
是 `\hat{}` $\hat{R_p}$ 嗎