Markdown Cheat Sheet
- 数学相关LaTeX表达
- 前言
- - 表 1: 数学模式重音符
  - 表2: 小写希腊字母
  - 表 3: 大写希腊字母
  - 表 4: 数学字母
  - 表 5: 运算符与函数
  - 表 6: 常用箭头
  - 表 7: 其他常用符号
  - 表8: 使用字体
  - 表9: 分段函数与公式对齐
  - - 分段函数
    - 对齐控制
    - 公式编号
  - 表X: 矩阵
  - - 普通矩阵
    - 带省略符号的Matrix
    - 向量
- Emoji
- - 表XI: Emoji
- Refs

Markdown Cheat Sheet

数学相关LaTeX表达

前言

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
a^\hat {a}a^	\hat{a}	aˇ\check{a}aˇ	\check{a}	a~\tilde{a}a~	\tilde{a}	aˊ\acute{a}aˊ	\acute{a}
aˋ\grave{a}aˋ	\grave{a}	a˙\dot {a}a˙	\dot{a}	aˉ\bar{a}aˉ	\bar{a}	a¨\ddot aa¨	\ddot{a}
a⃗\vec {a}a	\vec{a}	A^\widehat{A}A	\widehat{A}	A~\widetilde{A}A	\widetilde{A}	a˘\breve aa˘	\breve{a}
		A^\hat{A}A^	\hat{A}	A~\tilde{A}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
α\alphaα	\alpha	θ\thetaθ	\theta	υ\upsilonυ	\upsilon	$o $	o
β\betaβ	\beta	ϑ\varthetaϑ	\vartheta	π\piπ	\pi	ϕ\phiϕ	\phi
γ\gammaγ	\gamma	ι\iotaι	\iota	ϖ\varpiϖ	\varpi	φ\varphiφ	\varphi
δ\deltaδ	\delta	κ\kappaκ	\kappa	ρ\rhoρ	\rho	χ\chiχ	\chi
ϵ\epsilonϵ	\epsilon	λ\lambdaλ	\lambda	ϱ\varrhoϱ	\varrho	ψ\psiψ	\psi
ε\varepsilonε	\varepsilon	μ\muμ	\mu	σ\sigmaσ	\sigma	ω\omegaω	\omega
ζ\zetaζ	\zeta	ν\nuν	\nu	ς\varsigmaς	\varsigma	∇\nabla∇	\nabla
η\etaη	\eta	ξ\xiξ	\xi	τ\tauτ	\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
Γ\GammaΓ	\Gamma	Λ\LambdaΛ	\Lambda	KaTeX parse error: Undefined control sequence: \mit at position 7: \Sigma\̲m̲i̲t̲\Sigma	\Sigma\mit\Sigma	Ψ\PsiΨ	\Psi
Δ\DeltaΔ	\Delta	Ξ\XiΞ	\Xi	Υ\UpsilonΥ	\Upsilon	KaTeX parse error: Undefined control sequence: \mit at position 7: \Omega\̲m̲i̲t̲\Omega	\Omega\mit\Omega
Θ\ThetaΘ	\Theta	Π\PiΠ	\Pi	Φ\PhiΦ	\Phi

表 4: 数学字母

示例	代码
ABCdefxyzXYZ123\mathbf {ABCdefxyzXYZ123}ABCdefxyzXYZ123	\mathbf {ABCdefxyzXYZ123}
ABCdefxyzXYZ123\mathrm {ABCdefxyzXYZ123}ABCdefxyzXYZ123	\mathrm {ABCdefxyzXYZ123}
ABCdefxyzXYZ123\mathit {ABCdefxyzXYZ123}ABCdefxyzXYZ123	\mathit {ABCdefxyzXYZ123}
ABCdefxyzXYZ123\mathcal {ABCdefxyzXYZ123}ABCdefxyzXYZ123	\mathcal {ABCdefxyzXYZ123}
ABCdefxyzXYZ123\mathscr {ABCdefxyzXYZ123}ABCdefxyzXYZ123	\mathscr {ABCdefxyzXYZ123}
ABCdefxyzXYZ123\mathfrak {ABCdefxyzXYZ123}ABCdefxyzXYZ123	\mathfrak {ABCdefxyzXYZ123}
ABCdefxyzXYZ123\mathbb {ABCdefxyzXYZ123}ABCdefxyzXYZ123	\mathbb {ABCdefxyzXYZ123}
ABCdefxyzXYZ123\boldsymbol{ABCdefxyzXYZ123}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⋅yx\cdot{y}x⋅y	x\cdot{y}
⋃\bigcup⋃	\bigcup	⨁\bigoplus⨁	\bigoplus	x×yx\times {y}x×y	x\times {y}
⋁\bigvee⋁	\bigvee	⋂\bigcap⋂	\bigcap	∥w∥\left\\|w\right\\|∥w∥	**\left\
⋀\bigwedge⋀	\bigwedge	⨄\biguplus⨄	\biguplus	∭\iiint∭	\iiint
⨂\bigotimes⨂	\bigotimes	∮\oint∮	\oint	∬\iint∬	\iint
∫xdx\int x\,{\rm d}x∫xdx	\int x,{\rm d}x	⨆\bigsqcup⨆	\bigsqcup	⟮⟯\lgroup \rgroup⟮⟯	\lgroup \rgroup
∐\coprod∐	\coprod	⨀\bigodot⨀	\bigodot	∂\partial∂	\partial
det⁡\detdet	\det	max⁡\maxmax	\max	min⁡\minmin	\min
log⁡\loglog	\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⁡f∈H\min \limits_{f \in {H}}f∈Hmin	\min \limits_{f \in {H}}
⩽\leqslant⩽	\leqslant	⩾\geqslant⩾	\geqslant	KaTeX parse error: Undefined control sequence: \cal at position 1: \̲c̲a̲l̲ ̲{C} \equiv 1	\equiv
≈\thickapprox≈	\thickapprox	∼∼\thicksim \sim∼∼	\thicksim \sim	(AB)\left(\frac{A}{B}\right)(BA)	\left(\frac{A}{B}\right)
≠\neq=	\neq	∈\in∈	\in	=^\hat{=}=^	\hat{=}
±\pm±	\pm	a\sqrt{a}a	\sqrt{a}	≥≤\geq \leq≥≤	\geq \leq
$\perp $	\perp	∠\angle∠	\angle	∝\varpropto∝	\varpropto
∞\infty∞	\infty	g′g^\primeg′	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
ABCdefxyzXYZ123\rm {ABCdefxyzXYZ123}ABCdefxyzXYZ123	\rm {ABCdefXYZ123}	罗马体
ABCdefxyzXYZ123\it{ABCdefxyzXYZ123}ABCdefxyzXYZ123	\it{ABCdefXYZ123}	意大利体
ABCdefxyzXYZ123\bf{ABCdefxyzXYZ123}ABCdefxyzXYZ123	\bf{ABCdefXYZ123}	正粗体，黑体
KaTeX parse error: Undefined control sequence: \cal at position 1: \̲c̲a̲l̲ ̲{ABCdefxyzXYZ12…	\cal {ABCdefXYZ123}	花体
ABCdefXYZ123\sf{ABCdefXYZ123}ABCdefXYZ123	\sf{ABCdefXYZ123}	等线体
KaTeX parse error: Undefined control sequence: \mit at position 1: \̲m̲i̲t̲{ABCdefxyzXYZ12…	\mit{ABCdefXYZ123}	数字斜体
ABCdefxyzXYZ123\tt{ABCdefxyzXYZ123}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)={1x与y满足某一事实0否则f(x,y) = \begin{cases} 1 & x与y满足某一事实\\ 0 & 否则 \end{cases} f(x,y)={10x与y满足某一事实否则

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

L(w)=∑i=1N[yilog⁡π(xi)+(1−yi)log⁡(1−π(xi))]=∑i=1N[yilog⁡π(xi)1−π(xi)+log⁡(1−π(xi))]=∑i=1N[yi(w⋅xi)−log⁡(1+exp⁡(w⋅xi)]\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} L(w)=i=1∑N[yilogπ(xi)+(1−yi)log(1−π(xi))]=i=1∑N[yilog1−π(xi)π(xi)+log(1−π(xi))]=i=1∑N[yi(w⋅xi)−log(1+exp(w⋅xi)]

对齐控制

# 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
KaTeX parse error: No such environment: equation at position 8: \begin{̲e̲q̲u̲a̲t̲i̲o̲n̲}̲ \begin{aligned…
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
KaTeX parse error: No such environment: align at position 8: \begin{̲a̲l̲i̲g̲n̲}̲ L(w)&=\sum\lim…
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：

align
\nonumber的使用

表X: 矩阵

普通矩阵

M1(x)=[a01a0200],M2(x)=[b11b12b21b22]M3(x)=[c11c12c21c22],M4(x)=[1010]\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} M1(x)=[a010a020]M3(x)=[c11c21c12c22],M2(x)=[b11b21b12b22],M4(x)=[1100]

\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

XT=[x11⋯x1N⋮⋱⋮xM1⋯xMN]X^\mathrm T= \left[ \begin{matrix} x_{11} & \cdots & x_{1N} \\ \vdots & \ddots & \vdots \\ x_{M1} & \cdots & x_{MN} \\ \end{matrix} \right] XT=⎣⎢⎡x11⋮xM1⋯⋱⋯x1N⋮xMN⎦⎥⎤

% 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

KaTeX parse error: Got function '\newline' with no arguments as argument to '\begin{array}' at position 1: \̲n̲e̲w̲l̲i̲n̲e̲

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

abcde⏞fghij⏟commentklmn‾opqr‾stuv←wxyz→\overbrace{abcde}\underbrace{fghij}_{comment}\overline{klmn}\underline{opqr}\overleftarrow{stuv}\overrightarrow{wxyz} abcdecommentfghijklmnopqrstuvwxyz

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

Emoji

表XI: Emoji