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科研Tips(数学符号)

本文列举了常用数学符号以供平时查询,包括希腊字母、二元关系符、二元运算符。

1. 帽子和鞋子

命令效果
\hat{A}$\hat{A}$
\widehat{A}$\widehat{A}$
\tilde{A}$\tilde{A}$
\widetilde{A}$\widetilde{A}$
\overline{A}$\overline{A}$
\underline{A}$\underline{A}$
\overbrace{A-B}^{hat}$\overbrace{A-B}^{hat}$
\underbrace{A-B}_{foot}$\underbrace{A-B}_{foot}$
\sum_{i=1}$ \sum_{i=1} $
\sum\limits_{i=1}$ \sum\limits_{i=1} $
\mathop{max}_z$ \mathop{max}_z$
\mathop{max}\limits_z$ \mathop{max}\limits_z$
\mathop{\rm max}\limits_z$\mathop{\rm max}\limits_z$

2. 空格

命令效果解释
a \qquad bmmb$a \qquad bmmb$间隔两个 $m$ 的宽度
a \quad bmmb$a \quad bmb$间隔一个 $m$ 的宽度
a \ bmb$a \ bmb$间隔 1/3 个 $m$ 的宽度
a \; bmb$a \; bmb$间隔 2/7 个 $m$ 的宽度
a \, bmb$a \, bmb$间隔 1/6 个 $m$ 的宽度
abmb$abmb$没有间隔
a\!bmb$a!bmb$缩进 1/6 个 $m$ 的宽度(浏览器可能渲染异常)

3. 希腊字母

大写命令大写小写命令小写
\Alpha$\Alpha$\alpha$\alpha$
\Beta$\Beta$\beta$\beta$
\Gamma$\Gamma$\gamma$\gamma$
\Delta$\Delta$\delta$\delta$
\Epsilon$\Epsilon$\epsilon,\varepsilon$\epsilon,\varepsilon$
\Zeta$\Zeta$\zeta$\zeta$
\Eta$\Eta$\eta$\eta$
\Theta$\Theta$\theta$\theta$
\Iota$\Iota$\iota$\iota$
\Kappa$\Kappa$\kappa$\kappa$
\Lambda$\Lambda$\lambda$\lambda$
\Mu$\Mu$\mu$\mu$
\Xi$\Xi$\xi$\xi$
\Rho$\Rho$\rho,\varrho$\rho,\varrho$
\Sigma$\Sigma$\sigma$\sigma$
\Tau$\Tau$\tau$\tau$
\Upsilon$\Upsilon$\upsilon$\upsilon$
\Phi$\Phi$\phi,\varphi$\phi,\varphi$
\Chi$\Chi$\chi$\chi$
\Psi$\Psi$\psi$\psi$
\Omega$\Omega$\omega$\omega$

4. 二元关系符

命令符号 命令符号 命令符号
\leq, \le$\leq$ \geq, \ge$\geq$ \equiv$\equiv$
\ll$\ll$ \gg$\gg$ \doteq$\doteq$
\prec$\prec$ \succ$\succ$ \sim$\sim$
\preceq$\preceq$ \succeq$\succeq$ \simeq$\simeq$
\subset$\subset$ \supset$\supset$ \approx$\approx$
\subseteq$\subseteq$ \supseteq$\supseteq$ \cong$\cong$
\in$\in$ \ni,\owns$\ni$ \propto$\propto$
\vdash$\vdash$ \dashv$\dashv$ \models$\models$
\mid$\mid$ \parallel$\parallel$ \perp$\perp$
\smile$\smile$ \frown$\frown$ \asymp$\asymp$
:$:$ \notin$\notin$ \neq,\ne$\neq$

注意,有 3 个比较特殊的关系符,在使用时需要添加 latexsym 宏包:

命令符号 命令符号 命令符号
\sqsubseteq$\sqsubseteq$ \sqsupseteq$\sqsupseteq$ \bowtie$\bowtie$

5. 二元运算符

命令符号 命令符号 命令符号
\pm$\pm$ \mp$\mp$ \triangleleft$\triangleleft$
\cdot$\cdot$ \div$\div$ \triangleright$\triangleright$
\times$\times$ \setminus$\setminus$ \star$\star$
\cup$\cup$ \cap$\cap$ \ast$\ast$
\sqcup$\sqcup$ \sqcap$\sqcap$ \circ$\circ$ (上标可作度$^{\circ}$)
\vee, \lor$\vee$ \wedge, \land$\wedge$ \bullet$\bullet$
\oplus$\oplus$ \ominus$\ominus$ \diamond$\diamond$
\odot$\odot$ \oslash$\oslash$ \uplus$\uplus$
\otimes$\otimes$ \bigcirc$\bigcirc$ \amalg$\amalg$
\bigtriangleup$\bigtriangleup$ \bigtriangledown$\bigtriangledown$ \dagger$\dagger$
\ddagger$\ddagger$ \wr$\wr$   

其中,有 4 个特殊符号需要添加 latexsym 宏包:

命令符号 命令符号
\lhd$\lhd$ \rhd$\rhd$
\unlhd$\unlhd$ \unrhd$\unrhd$

6. 大尺寸运算符

命令符号 命令符号 命令符号
\sum$\sum$ \bigcup$\bigcup$ \bigvee$\bigvee$
\prod$\prod$ \bigcap$\bigcap$ \bigwedge$\bigwedge$
\coprod$\coprod$ \bigsqcup$\bigsqcup$ \biguplus$\biguplus$
\bigoplus$\bigoplus$ \bigotimes$\bigotimes$ \bigodot$\bigodot$
\int$\int$ \oint$\oint$   

7. 箭头

命令符号 命令符号 命令符号
\leftarrow, \gets$\leftarrow$ \longleftarrow$\longleftarrow$ \uparrow$\uparrow$
\rightarrow, \to$\rightarrow$ \longrightarrow$\longrightarrow$ \downarrow$\downarrow$
\leftrightarrow$\leftrightarrow$ \longleftrightarrow$\longleftrightarrow$ \updownarrow$\updownarrow$
\Leftarrow$\Leftarrow$ \Longleftarrow$\Longleftarrow$ \Uparrow$\Uparrow$
\Rightarrow$\Rightarrow$ \Longrightarrow$\Longrightarrow$ \Downarrow$\Downarrow$
\Leftrightarrow$\Leftrightarrow$ \Longleftrightarrow$\Longleftrightarrow$ \Updownarrow$\Updownarrow$
\mapsto$\mapsto$ \longmapsto$\longmapsto$ \nearrow$\nearrow$
\hookleftarrow$\hookleftarrow$ \hookrightarrow$\hookrightarrow$ \searrow$\searrow$
\leftharpoonup$\leftharpoonup$ \rightharpoonup$\rightharpoonup$ \swarrow$\swarrow$
\leftharpoondown$\leftharpoondown$ \rightharpoondown$\rightharpoondown$ \nwarrow$\nwarrow$
\rightleftharpoons$\rightleftharpoons$ \iff$\iff$ \$\backslash$

其中,有 1 个特殊符号需要添加 latexsym 宏包:

命令符号
\leadsto$\leadsto$

8. 其它符号

命令符号 命令符号 命令符号
\cdots$\cdots$ \vdots$\vdots$ \ddots$\ddots$
\hbar$\hbar$ \ell$\ell$ \Re$\Re$
\aleph$\aleph$ \forall$\forall$ \partial$\partial$
\nabla$\nabla$ \infty$\infty$ \empty$\empty$
\bot$\bot$ \top$\top$ \varnothing$\varnothing$
\flat$\flat$ \natural$\natural$ \sharp$\sharp$
\prime$\prime$ \exists$\exists$ \angle$\angle$

9. 矩阵

无需 \begin{aligned} 的写法:

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a=\begin{matrix}
1 & 2 \\
3 & 4 \\
\end{matrix}
a=\begin{bmatrix}
1 & 2 \\
3 & 4 \\
\end{bmatrix}
a=\begin{pmatrix}
1 & 2 \\
3 & 4 \\
\end{pmatrix}
a=\begin{Bmatrix}
1 & 2 \\
3 & 4 \\
\end{Bmatrix}
a=\begin{vmatrix}
1 & 2 \\
3 & 4 \\
\end{vmatrix}
a=\begin{Vmatrix}
1 & 2 \\
3 & 4 \\
\end{Vmatrix}
\[a=\begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix},\ a=\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ \end{bmatrix},\ a=\begin{pmatrix} 1 & 2 \\ 3 & 4 \\ \end{pmatrix},\ a=\begin{Bmatrix} 1 & 2 \\ 3 & 4 \\ \end{Bmatrix},\ a=\begin{vmatrix} 1 & 2 \\ 3 & 4 \\ \end{vmatrix},\ a=\begin{Vmatrix} 1 & 2 \\ 3 & 4 \\ \end{Vmatrix}\]

方程组对齐的写法({l}-left,{c}-center,{r}-right):

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\left\{
\begin{array}{l}
\dot x_1(t) = x_2(t)\\
\dot x_2(t) = x_1(t){\rm cos}x_2(t)-x_3(t)\\
\dot x_3(t) = x_1(t)x_3(t) + (1+\varepsilon {\rm sin}x_3(t))u(t)
\end{array}
\right.

\(\left\{ \begin{array}{l} \dot x_1(t) = x_2(t)\\ \dot x_2(t) = x_1(t){\rm cos}x_2(t)-x_3(t)\\ \dot x_3(t) = x_1(t)x_3(t) + (1+\varepsilon {\rm sin}x_3(t))u(t) \end{array} \right.\)

方程组对齐的矩阵写法(居中对齐):

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\left\{
\begin{matrix}
\dot x_1(t) = x_2(t)\\
\dot x_2(t) = x_1(t){\rm cos}x_2(t)-x_3(t)\\
\dot x_3(t) = x_1(t)x_3(t) + (1+\varepsilon {\rm sin}x_3(t))u(t)
\end{matrix}
\right.

\(\left\{ \begin{matrix} \dot x_1(t) = x_2(t)\\ \dot x_2(t) = x_1(t){\rm cos}x_2(t)-x_3(t)\\ \dot x_3(t) = x_1(t)x_3(t) + (1+\varepsilon {\rm sin}x_3(t))u(t) \end{matrix} \right.\)

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