Latex 数学符号 汇总

Latex Math Symbol Cheat Sheet

ZingLix August 23, 2017

Latex 的一大优点就是其可以写出优美的数学公式,本博客也使用 MathJax 来得到 Latex 中数学公式的效果。但是由于其有自己的语法,所以写了这篇文章以整理数学公式相关的内容。

由于本文中公式较多,所以可能需要些许渲染的时间。

常见公式

名称 代码 效果
上下标 _1^2X_3^4 \(_1^2X_3^4\)
组合数 \mathrm{C}_n^r \(\mathrm{C}_n^r\)
排列数 \mathrm{P}_n^r \(\mathrm{P}_n^r\)
上划线 \overline{abc} \(\overline{abc}\)
下划线 \underline{abc} \(\underline{abc}\)
求和 \sum_{k=1}^N k^2 \(\sum\limits_{k=1}^N k^2\)
求积 \prod_{i=1}^N x_i \(\prod\limits_{i=1}^N x_i\)
极限 \lim_{n \to \infty}n \(\lim\limits_{n \to \infty}n\)
根号 \sqrt[n]{x}| \(\sqrt[n]{x}\)
上括号 \overbrace{a+b+\cdots+z}^26 \(\overbrace{a+b+\cdots+z}^{26}\)
下括号 \underbrace{a+b+\cdots+z}_26 \(\underbrace{a+b+\cdots+z}_{26}\)
向量 \overrightarrow{AB} \(\overrightarrow{AB}\)

分数

分数最普通的形式为\frac{x}{y},也可以用\tfrac{x}{y}来得到较小的分数。

\[\frac{x}{y}\ \ \tfrac{x}{y}\]

\frac{x}{1+\frac{y}}可以得到连分数,但是使用\cfrac代替可以得到更大的分数。

\[\frac{2}{c + \frac{2}{d + \frac{2}{4}}} \ \ \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}}\]

矩阵

矩阵首尾以\begin{matrix}\end{matrix}标记,各元素以&分隔,以\\换行。

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\begin{matrix}
a_{11} & \cdots & a_{1n}  \\
\vdots & \ddots & \vdots  \\
a_{n1} & \cdots & a_{nn}
\end{matrix}

如上则是一个矩阵的代码,可以得到如下的效果。

\[\begin{matrix} a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{n1} & \cdots & a_{nn} \end{matrix}\]

此外对于{matrix}中 matrix 可以替换成如下内容,以得到不同的边框。

替换内容 效果 替换内容 效果
vmatrix \(\begin{vmatrix}a & b \\c & d\end{vmatrix}\) Vmatrix \(\begin{Vmatrix}a & b \\c & d\end{Vmatrix}\)
bmatrix \(\begin{bmatrix}a & b \\c & d\end{bmatrix}\) Bmatrix \(\begin{Bmatrix}a & b \\c & d\end{Bmatrix}\)
pmatrix \(\begin{pmatrix}a & b \\c & d\end{pmatrix}\) smallmatrix \(\begin{smallmatrix}a & b \\c & d\end{smallmatrix}\)

分段函数 & 方程组

首尾以\begin{cases}\end{cases}标记,各元素以&分隔,以\\换行。

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f(x) =
\begin{cases}
x,  & x\ge0 \\
-x, & x<0
\end{cases}

可以得到如下效果。

\[f(x) = \begin{cases} x, & x\ge0 \\ -x, & x<0 \end{cases}\]

如下所示,可以对上面的稍加修改,

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\begin{cases}
x+y=1 \\
3x+4y=5 \\
\end{cases}

便可以得到方程组的形式。

\[\begin{cases} x+y=1 \\ 3x+4y=5 \\ \end{cases}\]

多行等式

首尾以\begin{align}\end{align}标记,各元素以&分隔,以\\换行。

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\begin{align}
(x+y)^3 & = (x+y)^2(x+y)
& = (x+y)(x+y)(x+y)
\end{align}

实际效果如下。

\[\begin{align} (x+y)^3 & = (x+y)^2(x+y)\\ & = (x+y)(x+y)(x+y)\\ \end{align}\]

空格

功能 代码 效果 宽度
2个quad空格 \qquad \(A\qquad B\) \(2m\)
quad空格 \quad \(A\quad B\) \(m\)
大空格 \ \(A\ B\) \(\frac{m}{3}\)
中等空格 \; \(A\;B\) \(\frac{2m}{7}\)
小空格 \, \(A\,B\) \(\frac{m}{6}\)
没有空格 \(AB\) \(0\)
紧贴 \! \(A\!B\) \(-\frac{m}{6}\)

括号

\left\right来控制左右括号。

功能 语法 显示
小括号 \left( \frac{a}{b} \right) \(\left( \frac{a}{b} \right)\)
中括号 \left[ \frac{a}{b} \right] \(\left[ \frac{a}{b} \right]\)
大括号 \left\{ \frac{a}{b} \right\} \(\left\{ \frac{a}{b} \right\}\)
角括号 \left \langle \frac{a}{b} \right \rangle \(\left\langle \frac{a}{b} \right \rangle\)
双竖线 \left\Vert \frac{a}{b} \right\Vert \(\left\Vert \frac{a}{b} \right\Vert\)
绝对值 \left\| \frac{a}{b} \right \| \(\left| \frac{a}{b} \right |\)
向下取整 \left \lfloor \frac{a}{b} \right \rfloor \(\left \lfloor \frac{a}{b} \right \rfloor\)
向上取整 \left \lceil \frac{c}{d} \right \rceil \(\left \lceil \frac{c}{d} \right \rceil\)
斜线与反斜线 \left / \frac{a}{b} \right \backslash \(\left / \frac{a}{b} \right \backslash\)
上下箭头 \left \uparrow \frac{a}{b} \right \downarrow \(\left \uparrow \frac{a}{b} \right \downarrow\)
上下箭头 \left \Uparrow \frac{a}{b} \right \Downarrow \(\left \Uparrow \frac{a}{b} \right \Downarrow\)

括号同时可以用\big \Big \bigg \Bigg修饰。

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\Bigg( \bigg[ \Big\{ \big\langle\left| \frac{a}{b} \right| \big\rangle \Big\} \bigg] \Bigg)

如上代码可以得到如下效果。

\[\Bigg( \bigg[ \Big\{ \big\langle\left| \frac{a}{b} \right| \big\rangle \Big\} \bigg] \Bigg)\]

微积分

代码 效果 代码 效果 代码 效果
\nabla \(\nabla\) \partial{x} \(\partial{x}\) \mathrm{d}x \(\mathrm{d}x\)
\dot{x} \(\dot{x}\) \ddot{y} \(\ddot{y}\) \frac{\mathrm{d}y}{\mathrm{d}x} \(\frac{\mathrm{d}y}{\mathrm{d}x}\)
f\prime(x) \(f\prime(x)\) \int_{-N}^{N} \(\int_{-N}^{N}\) \iint_{-N}^{N} \(\iint_{-N}^{N}\)
\iiint_{-N}^{N} \(\iiint_{-N}^{N}\) \iiiint_{-N}^{N} \(\iiint_{-N}^{N}\) \oint_{C} \(\oint_{C}\)

特殊字体

名称 代码 效果
黑板粗体 \mathbb{ONLY\ UPPERCASE} \(\mathbb{ONLY\ UPPERCASE}\)
正粗体 \mathbf{abcDEFGHI012} \(\mathbf{abcDEFGHI012}\)
斜粗体 \boldsymbol{abcDEFGHI012} \(\boldsymbol{abcDEFGHI012}\)
斜体数字 \mathit{0123456789} \(\mathit{0123456789}\)
罗马体 \mathrm{012} \mbox{abc} \operatorname{ABC} \(\mathrm{012} \mbox{abc} \operatorname{ABC}\)
哥特体 \mathfrak{abcDEFGHI012} \(\mathfrak{abcDEFGHI012}\)
手写体 \mathcal{abcDEFGHI012} \(\mathcal{abcDEFGHI012}\)
希伯来字母 \aleph\beth\gimel\daleth \(\aleph\beth\gimel\daleth\)

字符标记

代码 效果 代码 效果 代码 效果
\acute{a} \(\acute{a}\) \grave{a} \(\grave{a}\) \hat{a} \(\hat{a}\)
\tilde{a} \(\tilde{a}\) \breve{a} \(\breve{a}\) \check{a} \(\check{a}\)
\bar{a} \(\bar{a}\) \ddot{a} \(\ddot{a}\) \dot{a} \(\dot{a}\)

常见函数

代码 效果 代码 效果 代码 效果
\sin \(\sin\) \cos \(\cos\) \tan \(\tan\)
\sec \(\sec\) \csc \(\csc\) \cot \(\cot\)
\arcsin \(\arcsin\) \arccos \(\arccos\) \arctan \(\arctan\)
\sinh \(\sinh\) \cosh \(\cosh\) \tanh \(\tanh\)
\coth \(\coth\) \lim \(\lim\) \limsup \(\limsup\)
\liminf \(\liminf\) \min \(\min\) \max \(\max\)
\inf \(\inf\) \sup \(\sup\) \exp \(\exp\)
\ln \(\ln\) \lg \(\lg\) \log \(\log\)
\log_{10} \(\log_{10}\) \ker \(\ker\) \deg \(\deg\)
\gcd \(\gcd\) \Pr \(\Pr\) \det \(\det\)
\hom \(\hom\) \arg \(\arg\) \dim \(\dim\)
\bmod \(\bmod\)        

二元运算符

代码 效果 代码 效果 代码 效果
+ \(+\) - \(-\) \pm \(\pm\)
\mp \(\mp\) \dotplus \(\dotplus\) \times \(\times\)
\div \(\div\) \divideontimes \(\divideontimes\) \backslash \(\backslash\)
\cdot \(\cdot\) \ast \(\ast\) \star \(\star\)
\circ \(\circ\) \bullet \(\bullet\) \boxplus \(\boxplus\)
\boxminus \(\boxminus\) \boxtimes \(\boxtimes\) \boxdot \(\boxdot\)
\oplus \(\oplus\) \ominus \(\ominus\) \otimes \(\otimes\)
\oslash \(\oslash\) \odot \(\odot\) \circleddash \(\circleddash\)
\circledcirc \(\circledcirc\) \circledast \(\circledast\) \bigoplus \(\bigoplus\)
\bigotimes \(\bigotimes\) \bigodot \(\bigodot\) \equiv \(\equiv\)

集合

代码 效果 代码 效果 代码 效果
\forall \(\forall\) \exists \(\exists\) \emptyset \(\emptyset\)
\in \(\in\) \ni \(\ni\) \notin \(\notin\)
\subset \(\subset\) \subseteq \(\subseteq\) \supset \(\supset\)
\supseteq \(\supseteq\) \bigcap \(\bigcap\) \cup \(\cup\)
\bigcup \(\bigcup\) \biguplus \(\biguplus\) \setminus \(\setminus\)
\smallsetminus \(\smallsetminus\) \sqsubset \(\sqsubset\) \sqsubseteq \(\sqsubseteq\)
\sqsupset \(\sqsupset\) \sqsupseteq \(\sqsupseteq\) \sqcap \(\sqcap\)
\sqcup \(\sqcup\) \bigsqcup \(\bigsqcup\) \cap \(\cap\)
\varnothing \(\varnothing\) \cap \(\cap\)    
\nsubseteq \(\nsubseteq\) \nsupseteq \(\nsupseteq\) \nsubseteqq \(\nsubseteqq\)
\nsupseteqq \(\nsupseteqq\) \subseteqq \(\sqsubset\) \supseteqq \(\sqsubseteq\)
\sqsupset \(\sqsupset\) \sqsupseteq \(\sqsupseteq\) \sqcap \(\sqcap\)

逻辑运算符

代码 效果 代码 效果 代码 效果
\land \(\land\) \wedge \(\wedge\) \bigwedge \(\bigwedge\)
\bar{q} \(\bar{A}\) \to \(\to\) \lor \(\lor\)
\vee \(\vee\) \bigvee \(\bigvee\) \lnot \(\lnot\)
\neg \(\neg\) \And \(\And\)    

关系运算符

代码 效果 代码 效果 代码 效果
\sim \(\sim\) \approx \(\approx\) \simeq \(\simeq\)
\cong \(\cong\) \dot= \(\dot=\) \gtrapprox \(\gtrapprox\)
< \(<\) \le \(\le\) \ll \(\ll\)
\gg \(\gg\) \ge \(\ge\) > \(>\)
\equiv \(\equiv\) \not\equiv \(\not\equiv\) \ne \(\ne\)
\mbox{or} \(\mbox{or}\) \neq \(\neq\) \propto \(\propto\)
\lessapprox \(\lessapprox\) \lesssim \(\lesssim\) \eqslantless \(\eqslantless\)
\leqslant \(\leqslant\) \leqq \(\leqq\) \geqq \(\geqq\)
\geqslant \(\geqslant\) \eqslantgtr \(\eqslantgtr\) \gtrsim \(\gtrsim\)

几何符号

代码 效果 代码 效果 代码 效果
\Diamond \(\Diamond\) \Box \(\Box\) \triangle \(\triangle\)
\angle \(\angle\) \perp \(\perp\) \mid \(\mid\)
\nmid \(\nmid\) \| \(|\) 45^\circ \(45^\circ\)
\sphericalangle \(\sphericalangle\) \bigtriangledown \(\bigtriangledown\)    

希腊字母

代码 效果 代码 效果 代码 效果 代码 效果
\alpha \(\alpha\) \theta \(\theta\) o \(o\) \tau \(\tau\)
\beta \(\beta\) \vartheta \(\vartheta\) \pi \(\pi\) \upsilon \(\upsilon\)
\gamma \(\gamma\) \iota \(\iota\) \varpi \(\varpi\) \phi \(\phi\)
\delta \(\delta\) \kappa \(\kappa\) \rho \(\rho\) \varphi \(\varphi\)
\epsilon \(\epsilon\) \lambda \(\lambda\) \varrho \(\varrho\) \chi \(\chi\)
\varepsilon \(\varepsilon\) \mu \(\mu\) \sigma \(\sigma\) \psi \(\psi\)
\zeta \(\zeta\) \nu \(\nu\) \varsigma \(\varsigma\) \omega \(\omega\)
\eta \(\eta\) \xi \(\xi\)        
\Gamma \(\Gamma\) \Lambda \(\Lambda\) \Sigma \(\Sigma\) \Psi \(\Psi\)
\Delta \(\Delta\) \Xi \(\Xi\) \Upsilon \(\Upsilon\) \Omega \(\Omega\)
\Theta \(\Theta\) \Pi \(\Pi\) \Phi \(\Phi\)    

箭头

代码 效果 代码 效果 代码 效果
\leftarrow \(\leftarrow\) \rightarrow \(\rightarrow\) \nleftarrow \(\nleftarrow\)
\nrightarrow \(\nrightarrow\) \leftrightarrow \(\leftrightarrow\) \nleftrightarrow \(\nleftrightarrow\)
\longleftarrow \(\longleftarrow\) \longrightarrow \(\longrightarrow\) \longleftrightarrow \(\longleftrightarrow\)
\leftarrow \(\leftarrow\) \rightarrow \(\rightarrow\) \nleftarrow \(\nleftarrow\)
\nrightarrow \(\nrightarrow\) \leftrightarrow \(\leftrightarrow\) \nleftrightarrow \(\nleftrightarrow\)
\longleftarrow \(\longleftarrow\) \longrightarrow \(\longrightarrow\) \longleftrightarrow \(\longleftrightarrow\)
\Leftarrow \(\Leftarrow\) \Rightarrow \(\Rightarrow\) \nLeftarrow \(\nLeftarrow\)
\nRightarrow \(\nRightarrow\) \Leftrightarrow \(\Leftrightarrow\) \nLeftrightarrow \(\nLeftrightarrow\)
\Longleftarrow \(\Longleftarrow\) \Longrightarrow \(\Longrightarrow\) \Longleftrightarrow \(\Longleftrightarrow\)
\Leftarrow \(\Leftarrow\) \Rightarrow \(\Rightarrow\) \nLeftarrow \(\nLeftarrow\)
\nRightarrow \(\nRightarrow\) \Leftrightarrow \(\Leftrightarrow\) \nLeftrightarrow \(\nLeftrightarrow\)
\Longleftarrow \(\Longleftarrow\) \Longrightarrow \(\Longrightarrow\) \Longleftrightarrow \(\Longleftrightarrow\)
\uparrow \(\uparrow\) \downarrow \(\downarrow\) \updownarrow \(\updownarrow\)
\Uparrow \(\Uparrow\) \Downarrow \(\Downarrow\) \Updownarrow \(\Updownarrow\)
\nearrow \(\nearrow\) \searrow \(\searrow\) \swarrow \(\swarrow\)
\nwarrow \(\nwarrow\) \uparrow \(\uparrow\) \downarrow \(\downarrow\)
\updownarrow \(\updownarrow\) \Uparrow \(\Uparrow\) \Downarrow \(\Downarrow\)
\Updownarrow \(\Updownarrow\) \nearrow \(\nearrow\) \searrow \(\searrow\)
\swarrow \(\swarrow\) \nwarrow \(\nwarrow\) \rightharpoonup \(\rightharpoonup\)
\rightharpoondown \(\rightharpoondown\) \leftharpoonup \(\leftharpoonup\) \leftharpoondown \(\leftharpoondown\)
\upharpoonleft \(\upharpoonleft\) \upharpoonright \(\upharpoonright\) \downharpoonleft \(\downharpoonleft\)
\downharpoonright \(\downharpoonright\) \rightleftharpoons \(\rightleftharpoons\) \leftrightharpoons \(\leftrightharpoons\)
\rightharpoonup \(\rightharpoonup\) \rightharpoondown \(\rightharpoondown\) \leftharpoonup \(\leftharpoonup\)
\leftharpoondown \(\leftharpoondown\) \upharpoonleft \(\upharpoonleft\) \upharpoonright \(\upharpoonright\)
\downharpoonleft \(\downharpoonleft\) \downharpoonright \(\downharpoonright\) \rightleftharpoons \(\rightleftharpoons\)
\leftrightharpoons \(\leftrightharpoons\) \curvearrowleft \(\curvearrowleft\) \circlearrowleft \(\circlearrowleft\)
\Lsh \(\Lsh\) \upuparrows \(\upuparrows\) \rightrightarrows \(\rightrightarrows\)
\rightleftarrows \(\rightleftarrows\) \Rrightarrow \(\Rrightarrow\) \rightarrowtail \(\rightarrowtail\)
\looparrowright \(\looparrowright\) \curvearrowleft \(\curvearrowleft\) \circlearrowleft \(\circlearrowleft\)
\Lsh \(\Lsh\) \upuparrows \(\upuparrows\) \rightrightarrows \(\rightrightarrows\)
\rightleftarrows \(\rightleftarrows\) \Rrightarrow \(\Rrightarrow\) \rightarrowtail \(\rightarrowtail\)
\looparrowright \(\looparrowright\) \curvearrowright \(\curvearrowright\) \circlearrowright \(\circlearrowright\)
\Rsh \(\Rsh\) \downdownarrows \(\downdownarrows\) \leftleftarrows \(\leftleftarrows\)
\leftrightarrows \(\leftrightarrows\) \Lleftarrow \(\Lleftarrow\) \leftarrowtail \(\leftarrowtail\)
\looparrowleft \(\looparrowleft\) \curvearrowright \(\curvearrowright\) \circlearrowright \(\circlearrowright\)
\Rsh \(\Rsh\) \downdownarrows \(\downdownarrows\) \leftleftarrows \(\leftleftarrows\)
\leftrightarrows \(\leftrightarrows\) \Lleftarrow \(\Lleftarrow\) \leftarrowtail \(\leftarrowtail\)
\looparrowleft \(\looparrowleft\) \mapsto \(\mapsto\) \longmapsto \(\longmapsto\)
\hookrightarrow \(\hookrightarrow\) \hookleftarrow \(\hookleftarrow\) \multimap \(\multimap\)
\leftrightsquigarrow \(\leftrightsquigarrow\) \rightsquigarrow \(\rightsquigarrow\)    

此外还有几个可以在箭头上下方写字的箭头。

代码 效果
\xleftarrow[下方公式]{上方公式} \(A\xleftarrow[下方公式]{上方公式}B\)
\xrightarrow[下方公式]{上方公式} \(A\xrightarrow[下方公式]{上方公式}B\)
\underrightarrow{演示} \(A\underrightarrow{演示}B\)
\underleftarrow{演示} \(A\underleftarrow{演示}B\)
\underleftrightarrow{演示} \(A\underleftrightarrow{演示}B\)

其他各类符号

代码 效果 代码 效果 代码 效果
\ldots \(\ldots\) \cdots \(\cdots\) \vdots \(\vdots\)
\ddots \(\ddots\) \aleph \(\aleph\) \prime \(\prime\)
\infty \(\infty\) \hbar \(\hbar\) \Box$ \(\Box\)
\imath \(\imath\) \jmath \(\jmath\) \surd \(\surd\)
\flat \(\flat\) \triangle \(\triangle\) \ell \(\ell\)
\top \(\top\) \natural \(\natural\) \clubsuit \(\clubsuit\)
\wp \(\wp\) \bot \(\bot\) \sharp \(\sharp\)
\diamondsuit \(\diamondsuit\) \Re \(\Re\) \| \(|\)
\backslash \(\backslash\) \heartsuit \(\heartsuit\) \Im \(\Im\)
\spadesuit \(\spadesuit\) \mho \(\mho\)    

主要根据 维基百科 制作