# Markdown Cheat Sheet ![Hits](https://www.smirkcao.info/hit_gits/Lihang/math_markdown.md) [TOC] ## 数学相关LaTeX表达 ## 前言 后面介绍的内容是$\LaTeX$排版的数学符号的内容，不止一次有人强调中文版的Wikipedia并不是英文版内容的翻译，并不是。可以对比下参考部分的两个页面，我觉得中文页面做的不错，这两个页面里面关于垂直，貌似有那么点不同。 ### 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** | | | ### 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** | $\Sigma\mit\Sigma$ | **\Sigma\mit\Sigma** | $\Psi$ | **\Psi** | | $\Delta$ | **\Delta** |$\Xi$ | **\Xi** | $\Upsilon$ | **\Upsilon** | $\Omega\mit\Omega$ | **\Omega\mit\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\\|w\right\|** | | $\bigwedge$ | \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 | | $\thickapprox$ | \thickapprox | $\thicksim \sim$ | \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** | 注意**\bot**和**\perp**的区别，垂直是**\perp** ### 表8: 使用字体 | 示例 | 代码 | 备注 | | - | - | - | | $\rm {ABCdefxyzXYZ123}$ | \rm {ABCdefXYZ123} | 罗马体 | | $\it{ABCdefxyzXYZ123}$ | \it{ABCdefXYZ123} | 意大利体 | | $\bf{ABCdefxyzXYZ123}$ | \bf{ABCdefXYZ123} | 正粗体，黑体 | | $\cal {ABCdefxyzXYZ123}$ | \cal {ABCdefXYZ123} | 花体 | | $\sf{ABCdefXYZ123}$ | \sf{ABCdefXYZ123} | 等线体 | | $\mit{ABCdefxyzXYZ123}$ | \mit{ABCdefXYZ123} | **数字斜体** | | $\tt{ABCdefxyzXYZ123}$ | \tt{ABCdefXYZ123} | 打印机字体 | ### 表9: 分段函数与公式对齐 #### 分段函数 示例 $$ f(x,y) = \begin{cases} 1 & x与y满足某一事实\\ 0 & 否则 \end{cases} $$ ```latex # 代码 f(x,y) = \begin{cases} 1 & x与y满足某一事实\\ 0 & 否则 \end{cases} ``` $$ \begin{aligned} L(w)&=\sum\limits^{N}_{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\\&=\sum\limits^{N}_{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\\&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})] \end{aligned} $$ #### 对齐控制 ```latex # 代码 # 通过\begin{aligned}\end{aligned}控制对齐, 使用&表示对齐点. \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 ```latex \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 ```latex \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 1. \nonumber的使用 ### 表X: 矩阵 #### 普通矩阵 $$ \begin{aligned} M_1(x)= \begin{bmatrix} &a_{01}&a_{02}\\ &0&0 \end{bmatrix} &,M_2(x)= \begin{bmatrix} &b_{11}&b_{12}\\ &b_{21}&b_{22} \end{bmatrix} \\ M_3(x)= \begin{bmatrix} &c_{11}&c_{12}\\ &c_{21}&c_{22} \end{bmatrix} &,M_4(x)= \begin{bmatrix} &1&0\\ &1&0 \end{bmatrix} \end{aligned} $$ ```latex \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 $$ X^\mathrm T= \left[ \begin{matrix} x_{11} & \cdots & x_{1N} \\ \vdots & \ddots & \vdots \\ x_{M1} & \cdots & x_{MN} \\ \end{matrix} \right] $$ ```latex % 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 $$ \left[ \begin{array} \\2 \\3 \end{array} \right] $$ ```latex \left[ \begin{array} \\2 \\3 \end{array} \right] ``` $$ \overbrace{abcde}\underbrace{fghij}_{comment}\overline{klmn}\underline{opqr}\overleftarrow{stuv}\overrightarrow{wxyz} $$ ```tex \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 | ## Refs 1. [Markdown 数学符号速查](https://www.cnblogs.com/blog4ljy/p/9066624.html) 2. [Cmd Markdown公式指导手册](https://www.zybuluo.com/codeep/note/163962) 3. [Equals_Sign](https://en.wikipedia.org/wiki/Equals_sign#Other_related_symbols) 4. [Emoji](https://gist.github.com/rxaviers/7360908) 5. [Short Math Guide for LaTeX](http://ctan.math.utah.edu/ctan/tex-archive/info/short-math-guide/short-math-guide.pdf) 6. [List of Mathematical Symbols](https://en.wikipedia.org/wiki/List_of_mathematical_symbols) 7. [数学公式](https://zh.wikipedia.org/wiki/Help:数学公式) 8. [Matplotlib Math Text](https://matplotlib.org/tutorials/text/mathtext.html)