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2026-02-04 Others/06.实用工具 Hongwei Zhao

表 1: 数学模式重音符

示例 代码 示例 代码 示例 代码 示例 代码
\hat {a} \hat{a} \check{a} \check{a} \tilde{a} \tilde{a} \acute{a} \acute{a}
\grave{a} \grave{a} \dot {a} \dot{a} \bar{a} \bar{a} \ddot a \ddot{a}
\vec {a} \vec{a} \widehat{A} \widehat{A} \widetilde{A} \widetilde{A} \breve a \breve{a}
\hat{A} \hat{A} \tilde{A} \tilde{A}

表 2: 小写希腊字母

示例 代码 示例 代码 示例 代码 示例 代码
\alpha \alpha \theta \theta \upsilon \upsilon o o
\beta \beta \vartheta \vartheta \pi \pi \phi \phi
\gamma \gamma \iota \iota \varpi \varpi \varphi \varphi
\delta \delta \kappa \kappa \rho \rho \chi \chi
\epsilon \epsilon \lambda \lambda \varrho \varrho \psi \psi
\varepsilon \varepsilon \mu \mu \sigma \sigma \omega \omega
\zeta \zeta \nu \nu \varsigma \varsigma \nabla \nabla
\eta \eta \xi \xi \tau \tau \Psi \Psi

表 3: 大写希腊字母

示例 代码 示例 代码 示例 代码 示例 代码
\Gamma \Gamma \Lambda \Lambda \Sigma \Sigma \Psi \Psi
\Delta \Delta \Xi \Xi \Upsilon \Upsilon \Omega \Omega
\Theta \Theta \Pi \Pi \Phi \Phi

表 4: 数学字母

示例 代码
\mathbf {ABCdefxyzXYZ123} \mathbf {ABCdefxyzXYZ123}
\mathrm {ABCdefxyzXYZ123} \mathrm {ABCdefxyzXYZ123}
\mathit {ABCdefxyzXYZ123} \mathit {ABCdefxyzXYZ123}
\mathcal {ABCdefxyzXYZ123} \mathcal {ABCdefxyzXYZ123}
\mathscr {ABCdefxyzXYZ123} \mathscr {ABCdefxyzXYZ123}
\mathfrak {ABCdefxyzXYZ123} \mathfrak {ABCdefxyzXYZ123}
\mathbb {ABCdefxyzXYZ123} \mathbb {ABCdefxyzXYZ123}
\boldsymbol{ABCdefxyzXYZ123} \boldsymbol{ABCdefxyzXYZ123}

表 5: 运算符与函数

示例 代码 示例 代码 示例 代码
\sum \sum \prod \prod x\cdot{y} x\cdot{y}
\bigcup \bigcup \bigoplus \bigoplus x\times {y} x\times {y}
\bigvee \bigvee \bigcap \bigcap \left|w\right| **\left\
\bigwedge \bigwedge \biguplus \biguplus \iiint \iiint
\bigotimes \bigotimes \oint \oint \iint \iint
\int x\,{\rm d}x \int x\,{\rm d}x \bigsqcup \bigsqcup \lgroup \rgroup \lgroup \rgroup
\coprod \coprod \bigodot \bigodot \partial \partial
\det \det \max \max \min \min
\log \log

表 6: 常用箭头

示例 代码 示例 代码 示例 代码
\leftarrow \leftarrow \rightarrow \rightarrow \leftrightarrow \leftrightarrow
\longleftarrow \longleftarrow \longrightarrow \longrightarrow \longleftrightarrow \longleftrightarrow
\Leftarrow \Leftarrow \Rightarrow \Rightarrow \Leftrightarrow \Leftrightarrow
\Longleftarrow \Longleftarrow \Longrightarrow \Longrightarrow \Longleftrightarrow \Longleftrightarrow
\uparrow \uparrow \downarrow \downarrow \updownarrow \updownarrow

表 7: 其他常用符号

示例 代码 示例 代码 示例 代码
\therefore \therefore \because \because \min \limits_{f \in {H}} \min \limits_{f \in {H}}
\leqslant \leqslant \geqslant \geqslant \cal {C} \equiv 1 \equiv
\thickapprox \approx \thicksim \sim \thicksim \sim \left(\frac{A}{B}\right) \left(\frac{A}{B}\right)
\neq \neq \in \in \hat{=} \hat{=}
\pm \pm \sqrt{a} \sqrt{a} \geq \leq \geq \leq
\perp \perp \angle \angle \varpropto \varpropto
\infty \infty g^\prime g^\prime \forall \forall
\exist \exist \bot \bot \top \top
\notin \notin \ldots \ldots \cdots \cdots
\ddots \ddots \bcancel{a = b + c} \bcancel{a = b + c}

注意\bot 和\perp 的区别，垂直是\perp

表 8: 分段函数与公式对齐

分段函数

示例


f(x,y) = \begin{cases}
1 & x与y满足某一事实\
0 & 否则
\end{cases}


\begin{aligned}
L(w)&=\sum\limits^{N}{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\&=\sum\limits^{N}{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})]
\end{aligned}

另外注意到前面的分段函数自动变好了，但是上面多行对齐的公式没有自动编号，如果需要自动编号，外面嵌入 equation


\begin{equation}
\begin{aligned}
L(w)&=\sum\limits^{N}{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\
&=\sum\limits^{N}{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\
&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})]
\end{aligned}
\end{equation}

代码如下

\begin{equation}
\begin{aligned}
L(w)&=\sum\limits^{N}_{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\\&=\sum\limits^{N}_{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\\&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})]
\end{aligned}
\end{equation}

公式编号

关于编号也可以通过行间公式做如下表达


\begin{align}
L(w)&=\sum\limits^{N}{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\
&=\sum\limits^{N}{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\nonumber\
&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})]
\end{align}

代码如下

\begin{align}
L(w)&=\sum\limits^{N}_{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\\
&=\sum\limits^{N}_{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\nonumber\\
&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})]
\end{align}

以上代码有两点需要注意体会：

  1. align
  2. \nonumber 的使用

表 9: 矩阵

普通矩阵


\begin{aligned}
M_1(x)=
\begin{bmatrix}
&a_{01}&a_{02}\
&0&0
\end{bmatrix}
&,M_2(x)=
\begin{bmatrix}
&b_{11}&b_{12}\
&b_{21}&b_{22}
\end{bmatrix}
\
M_3(x)=
\begin{bmatrix}
&c_{11}&c_{12}\
&c_{21}&c_{22}
\end{bmatrix}
&,M_4(x)=
\begin{bmatrix}
&1&0\
&1&0
\end{bmatrix}
\end{aligned}

\begin{aligned}
M_1(x)=
\begin{bmatrix}
&a_{01}&a_{02}\\
&0&0
\end{bmatrix}
&,M_2(x)=
\begin{bmatrix}
&b_{11}&b_{12}\\
&b_{21}&b_{22}
\end{bmatrix}
\\
M_3(x)=
\begin{bmatrix}
&c_{11}&c_{12}\\
&c_{21}&c_{22}
\end{bmatrix}
&,M_4(x)=
\begin{bmatrix}
&1&0\\
&1&0
\end{bmatrix}
\end{aligned}

带省略符号的 Matrix


X^\mathrm T=
\left[
\begin{matrix}
x_{11} & \cdots & x_{1N} \
\vdots & \ddots & \vdots \
x_{M1} & \cdots & x_{MN} \
\end{matrix}
\right]

% 这里稍微注意下转置符号， 《统计学习方法》中的转置用的是正体的T
% 可以参考 https://zhuanlan.zhihu.com/p/27490955 中关于转置写法的讨论。
X^\mathrm T=
\left[
\begin{matrix}
 x_{11} & \cdots & x_{1N}       \\
 \vdots & \ddots & \vdots       \\
 x_{M1} & \cdots & x_{MN}       \\
\end{matrix}
\right]

向量


\left[
\begin{array}
\2
\3
\end{array}
\right]

\left[
\begin{array}
\\2
\\3
\end{array}
\right]


\overbrace{abcde}\underbrace{fghij}_{comment}\overline{klmn}\underline{opqr}\overleftarrow{stuv}\overrightarrow{wxyz}

\overbrace{abcde}\underbrace{fghij}_{comment}\overline{klmn}\underline{opqr}\overleftarrow{stuv}\overrightarrow{wxyz}

Emoji

表 XI: Emoji

:smirk: smirk :smile:smile :laughing:laughing :blush:blush :smiley:smiley :heart_eyes:heart_eyes
😘kissing_heart :wink:wink :kissing:kissing :confused:confused :sweat:sweat :joy:joy
:sob:sob :cry:cry :angry:angry :yum:yum :mask:mask :sunglasses:sunglasses
:heartpulse:heartpulse :alien:alien :cupid:cupid :+1:+1 :cn:cn :shit:shit

Reference

  1. Markdown 数学符号速查
  2. Cmd Markdown 公式指导手册
  3. Equals_Sign
  4. Emoji
  5. Short Math Guide for LaTeX
  6. List of Mathematical Symbols
  7. 数学公式
  8. Matplotlib Math Text

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