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}
$\stackrel{`}{a}$	\grave{a}	$\dot{a}$	\dot{a}	$\overline{a}$	\bar{a}	$\ddot{a}$	\ddot{a}
$\overrightarrow{a}$	\vec{a}	$\hat{A}$	\widehat{A}	$\tilde{A}$	\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	$\varphi$	\phi
$\gamma$	\gamma	$\iota$	\iota	$\varpi$	\varpi	$\phi$	\varphi
$\delta$	\delta	$\kappa$	\kappa	$\rho$	\rho	$\chi$	\chi
$ϵ$	\epsilon	$\lambda$	\lambda	$\varrho$	\varrho	$\psi$	\psi
$\epsilon$	\varepsilon	$\mu$	\mu	$\sigma$	\sigma	$\omega$	\omega
$\zeta$	\zeta	$\nu$	\nu	$\varsigma$	\varsigma	$\mathrm{\nabla }$	\nabla
$\eta$	\eta	$\xi$	\xi	$\tau$	\tau	$\mathrm{\Psi }$	\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
$\mathrm{\Gamma }$	\Gamma	$\mathrm{\Lambda }$	\Lambda	$\mathrm{\Sigma }$	\Sigma	$\mathrm{\Psi }$	\Psi
$\mathrm{\Delta }$	\Delta	$\mathrm{\Xi }$	\Xi	$\mathrm{{\rm Y}}$	\Upsilon	$\mathrm{\Omega }$	\Omega
$\mathrm{\Theta }$	\Theta	$\mathrm{\Pi }$	\Pi	$\mathrm{\Phi }$	\Phi

表 4: 数学字母

示例	代码
$\mathbf{ABCdefxyzXYZ}\mathbf{123}$	\mathbf {ABCdefxyzXYZ123}
$\mathrm{ABCdefxyzXYZ}123$	\mathrm {ABCdefxyzXYZ123}
$\mathit{ABCdefxyzXYZ}\mathit{123}$	\mathit {ABCdefxyzXYZ123}
$\mathcal{ABCdefxyzXYZ}\mathcal{123}$	\mathcal {ABCdefxyzXYZ123}
$\mathcal{ABCdefxyzXYZ}\mathcal{123}$	\mathscr {ABCdefxyzXYZ123}
$\mathfrak{ABCdefxyzXYZ}\mathfrak{123}$	\mathfrak {ABCdefxyzXYZ123}
$\mathbb{ABCdefxyzXYZ}\mathbb{123}$	\mathbb {ABCdefxyzXYZ123}
$\mathit{A}\mathit{B}\mathit{C}\mathit{d}\mathit{e}\mathit{f}\mathit{x}\mathit{y}\mathit{z}\mathit{X}\mathit{Y}\mathit{Z}\mathbf{123}$	\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	$x\times y$	x\times {y}
$\bigvee$	\bigvee	$\bigcap$	\bigcap	$\Vert w\Vert$	**\left\
$\bigwedge$	\bigwedge	$⨄$	\biguplus	$\iiint$	\iiint
$⨂$	\bigotimes	$\oint$	\oint	$\iint$	\iint
$\int x\mathrm{d}x$	\int x,{\rm d}x	$⨆$	\bigsqcup	$⟮⟯$	\lgroup \rgroup
$\coprod$	\coprod	$⨀$	\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	$\to$	\rightarrow	$\leftrightarrow$	\leftrightarrow
$⟵$	\longleftarrow	$⟶$	\longrightarrow	$⟷$	\longleftrightarrow
$\Leftarrow$	\Leftarrow	$\Rightarrow$	\Rightarrow	$\iff$	\Leftrightarrow
$⟸$	\Longleftarrow	$⟹$	\Longrightarrow	$⟺$	\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	$\underset{f\in H}{min}$	\min \limits_{f \in {H}}
$⩽$	\leqslant	$⩾$	\geqslant	$\mathcal{C}\equiv \mathcal{1}$	\equiv
$\approx$	\approx	$\sim \sim$	\thicksim \sim	$\left(\frac{A}{B}\right)$	\left(\frac{A}{B}\right)
$\ne$	\neq	$\in$	\in	$\widehat{=}$	\hat{=}
$\pm$	\pm	$\sqrt{a}$	\sqrt{a}	$\ge \le$	\geq \leq
$\perp$	\perp	$\mathrm{\angle }$	\angle	$\propto$	\varpropto
$\mathrm{\infty }$	\infty	$g^{\prime }$	g^\prime	$\mathrm{\forall }$	\forall
$\text{exist}$	\exist	$\mathrm{\perp }$	\bot	$\mathrm{\top }$	\top
$\notin$	\notin	$\dots$	\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

$$f(x,y)=\{\begin{array}{ll}1& x\mathrm{与}y\mathrm{满}\mathrm{足}\mathrm{某}\mathrm{一}\mathrm{事}\mathrm{实}\\ 0& \mathrm{否}\mathrm{则}\end{array}$$$$\begin{array}{rl}L(w)& =\sum _{i=1}^N[y_i\log \pi (x_i)+(1-y_i)\log (1-\pi (x_i))]\\ & =\sum _{i=1}^N[y_i\log \frac{\pi (x_i)}{1-\pi (x_i)}+\log (1-\pi (x_i))]\\ & =\sum _{i=1}^N[y_i(w\cdot x_i)-\log (1+\exp (w\cdot x_i)]\end{array}$$

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

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

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

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

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

$$\begin{array}{rl}{M}_1(x)=\left[\begin{array}{ccc}& a_{01}& a_{02}\\ & 0& 0\end{array}\right]& ,M_2(x)=\left[\begin{array}{ccc}& b_{11}& b_{12}\\ & b_{21}& b_{22}\end{array}\right]\\ M_3(x)=\left[\begin{array}{ccc}& c_{11}& c_{12}\\ & c_{21}& c_{22}\end{array}\right]& ,M_4(x)=\left[\begin{array}{ccc}& 1& 0\\ & 1& 0\end{array}\right]\end{array}$$

\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

$$X^{\mathrm{T}}=\left[\begin{array}{ccc}{x}_{11}& \cdots & x_{1N}\\ ⋮& \ddots & ⋮\\ x_{M1}& \cdots & x_{MN}\end{array}\right]$$

% 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]

$$\overbrace{abcde}\underset{comment}{\underbrace{fghij}}\overline{klmn}\underset{―}{opqr}\overleftarrow{stuv}\overrightarrow{wxyz}$$

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

Emoji

表 XI: Emoji

😏 smirk	😄smile	😆laughing	😊blush	😃smiley	😍heart_eyes
😘kissing_heart	😉wink	😗kissing	😕confused	😓sweat	😂joy
😭sob	😢cry	😠angry	😋yum	😷mask	😎sunglasses
💗heartpulse	👽alien	💘cupid	👍+1	🇨🇳cn	💩shit

Reference

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