在論文和博客的寫作中，經常會用到Latex的語法來書寫數學公式，一份詳細的數學符號對照表必不可少，本文重寫了部分 Markdown 公式指導手冊 。
-1.求和積分的上下標位置
\sum\nolimits_{j=1}^{M} 上下標位於求和符號的水平右端，
\sum\limits_{j=1}^{M} 上下標位於求和符號的上下處，
\sum_{j=1}^{M} 對上下標位置沒有設定，會隨公式所處環境自動調整。
\[\sum\nolimits_{j=1}^{M}\\ \sum\limits_{j=1}^{M}\\ \sum_{j=1}^{M} \]
0.大括號公式和一般括號
大括號顯示
\left\{
\begin{array}{**lr**}
x=\dfrac{3\pi}{2}(1+2t)\cos(\dfrac{3\pi}{2}(1+2t)), & \\
y=s, & 0\leq s\leq L,|t|\leq1.\\
z=\dfrac{3\pi}{2}(1+2t)\sin(\dfrac{3\pi}{2}(1+2t)), &
\end{array}
\right.
\[\left\{ \begin{array}{**lr**} x=\dfrac{3\pi}{2}(1+2t)\cos(\dfrac{3\pi}{2}(1+2t)), & \\ y=s, & 0\leq s\leq L,|t|\leq1.\\ z=\dfrac{3\pi}{2}(1+2t)\sin(\dfrac{3\pi}{2}(1+2t)), & \end{array} \right. \]
F^{HLLC}=\left\{
\begin{array}{rcl}
F_L & & {0 < S_L}\\
F^*_L & & {S_L \leq 0 < S_M}\\
F^*_R & & {S_M \leq 0 < S_R}\\
F_R & & {S_R \leq 0}
\end{array} \right.
\[F^{HLLC}=\left\{ \begin{array}{rcl} F_L & & {0 < S_L}\\ F^*_L & & {S_L \leq 0 < S_M}\\ F^*_R & & {S_M \leq 0 < S_R}\\ F_R & & {S_R \leq 0} \end{array} \right. \]
1.常用公式
| 描述 | 寫法 | 效果展示 |
|---|---|---|
| 上下標 | a_1 / e_x | \(a_1/e_x\) |
| 平方根 | \sqrt{x} | \(\sqrt{x}\) |
| 上下方水平線 | \overline{m+n} / \underline{m+n} | \(\overline{m+n} /\underline{m+n}\) |
| 上下方大括號 | \overbrace{m+n} / \underbrace{m+n} | \(\overbrace{m+n} / \underbrace{m+n}\) |
| 向量 | \vec a | \(\vec a\) |
| 分數 | \frac{1}{2} | \(\frac{1}{2}\) |
| 求和 | \sum_{i=1}^n | \(\sum_{i=1}^n\) |
| 積分 | \int_0^{\pi/2} | \(\int_0^{\pi/2}\) |
| 累乘 | \prod_\epsilon | \(\prod_\epsilon\) |
| 優化 | \mathop{\arg\min}_{\theta} | \(\mathop{\arg\min}_{\theta}\) |
| 時間復雜度 | \mathcal{O}(1) | \(\mathcal{O}(1)\) |
1.1 大尺度運算符
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \(\sum\) | \sum | \(\bigcup\) | \bigcup | \(\bigvee\) | \bigvee | \(\bigoplus\) | \bigoplus |
| \(\prod\) | \prod | \(\bigcap\) | \bigcap | \(\bigwedge\) | \bigwedge | \(\bigotimes\) | \bigotimes |
| \(\coprod\) | \coprod | \(\bigsqcup\) | \bigsqcup | \(\bigodot\) | \bigodot | ||
| \(\int\) | \int | \(\oint\) | \oint | \(\biguplus\) | \biguplus |
另外 \overline 能覆蓋所有括號中的文本，\bar 長度只能覆蓋一個字母。
$\overline{\bigcup A_i} = \bigcap \overline A_i$
\[\overline{\bigcup A_i} = \bigcap \overline A_i \]
1.2 矩陣
需要 amsmath 宏包：
\[ \begin{pmatrix} a&b\\c&d \end{pmatrix} \quad
\begin{bmatrix} a&b\\c&d \end{bmatrix} \quad
\begin{Bmatrix} a&b\\c&d \end{Bmatrix} \quad
\begin{vmatrix} a&b\\c&d \end{vmatrix} \quad
\begin{Vmatrix} a&b\\c&d \end{Vmatrix} \]
\[\begin{pmatrix} a&b\\c&d \end{pmatrix} \quad \begin{bmatrix} a&b\\c&d \end{bmatrix} \quad \begin{Bmatrix} a&b\\c&d \end{Bmatrix} \quad \begin{vmatrix} a&b\\c&d \end{vmatrix} \quad \begin{Vmatrix} a&b\\c&d \end{Vmatrix} \]
使用 smallmatrix 環境，可以生成行內公式的小矩陣：
Marry has a little matrix $ ( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} )$
Marry has a little matrix $ ( \begin{smallmatrix} a&b\ c&d \end{smallmatrix} )$
1.3 括號
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \((\) | ( | \()\) | ) | \(\uparrow\) | \uparrow | \(\Uparrow\) | \Uparrow |
| \(\lbrack\) | \[ or \lbrack | \(\rbrack\) | \] or \rbrack | \(\downarrow\) | \downarrow | \(\Downarrow\) | \Downarrow |
| \(\\\{\) | \{ or \lbrace | \(\}\) | \} or \rbrace | \(\updownarrow\) | \updownarrow | \(\Updownarrow\) | \Updownarrow |
| \(\langle\) | \langle | \(\rangle\) | \rangle | $ | $ | | or \vert | \(\parallel\) |
| \(\lfloor\) | \lfloor | \(\rfloor\) | \rfloor | \(\lceil\) | \lceil | \(\rceil\) | \rceil |
| \(/\) | / | \(\backslash\) | \backslash | \(\lmoustache\) | \lmoustache | \(\rmoustache\) | \rmoustache |
| \(\lgroup\) | \lgroup | \(\rgroup\) | \rgroup | \(\bracevert\) | \bracevert | ||
| \(\arrowvert\) | \arrowvert | \(\Arrowvert\) | \Arrowvert |
- 不同大小的括號
\Bigg ( \bigg [ \Big \{\big \langle \left \vert \parallel \frac{a}{b} \parallel \right \vert \big \rangle \Big \} \bigg ] \Bigg ):
\[\Bigg ( \bigg [ \Big \{\big \langle \left \vert \parallel \frac{a}{b} \parallel \right \vert \big \rangle \Big \} \bigg ] \Bigg ): \]
- 自適應大小的括號
\left( \frac{a}{b} \right)：
\[\left( \frac{a}{b} \right) \]
- 單邊括號
\left . \frac{a}{b} \right \rbrace:
\[\left . \frac{a}{b} \right \rbrace \]
- 混合括號
\left \langle \psi \right \vert:
\[\left \langle \psi \right \vert \]
- 模括號
\pmod p\[\pmod m \]
1.4 空格
LaTex 在數學公式中的字符間隔是默認自動調整的，直接輸入空格會被忽略掉，當我們需要自定義字母間隔時，需要手動輸入空格：
| 空格 | 寫法 | 顯示 | 備注 |
|---|---|---|---|
| 兩個quad空格 | a \qquad b | \(a \qquad b\) | 兩個m的寬度 |
| quad空格 | a \quad b | \(a \quad b\) | 一個m的寬度 |
| 大空格 | a\ b | \(a\ b\) | 1/3m寬度 |
| 中等空格 | a;b | \(a\;b\) | 2/7m寬度 |
| 小空格 | a,b | \(a\,b\) | 1/6m寬度 |
| 沒有空格 | ab | \(ab\) | |
| 緊貼 | a!b | \(a!b\) | 縮進1/6m寬度 |
2. 重音符
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \(\hat{a}\) | \hat{a} | \(\check{a}\) | \check{a} | \(\tilde{a}\) | \tilde{a} | \(\acute{a}\) | \acute{a} |
| \(\grave{a}\) | \grave{a} | \(\dot{a}\) | \dot{a} | \(\ddot{a}\) | \ddot{a} | \(\breve{a}\) | \breve{a} |
| \(\bar{a}\) | \bar{a} | \(\vec{a}\) | \vec{a} | \(\widehat{A}\) | \widehat{A} | \(\widetilde{A}\) | \widetilde{A} |
3. 希臘字母
3.1 小寫希臘字母
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \(\alpha\) | \alpha | \(\theta\) | \theta | \(o\) | o | \(\upsilon\) | \upsilon |
| \(\beta\) | \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 | ||
| \(\eta\) | \eta | \(\xi\) | \xi | \(\tau\) | \tau |
3.2 大寫希臘字母
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \(\Gamma\) | \Gamma | \(\Lambda\) | \Lambda | \(\Sigma\) | \Sigma | \(\Psi\) | \Psi |
| \(\Delta\) | \Delta | \(\Xi\) | \Xi | \(\Upsilon\) | \Upsilon | \(\Omega\) | \Omega |
| \(\Theta\) | \Theta | \(\Pi\) | \Pi | \(\Phi\) | \Phi |
4. 二元符號
4.1 二元關系符
可以在下述的命令中加上 \not 來得到
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \(<\) | < | \(>\) | > | \(=\) | = | \(\le\) | \leq or \le |
| \(\ge\) | \geq or \ge | \(\equiv\) | \equiv | \(\ll\) | \ll | \(\gg\) | \gg |
| \(\doteq\) | \doteq | \(\prec\) | \prec | \(\succ\) | \succ | \(\sim\) | \sim |
| \(\preceq\) | \preceq | \(\succeq\) | \succeq | \(\simeq\) | \simeq | \(\approx\) | \approx |
| \(\subset\) | \subset | \(\supset\) | \supset | \(\subseteq\) | \subseteq | \(\supseteq\) | \supseteq |
| \(\sqsubset\) | \sqsubset | \(\sqsupset\) | \sqsupset | \(\sqsubseteq\) | \sqsubseteq | \(\sqsupseteq\) | \sqsupseteq |
| \(\cong\) | \cong | \(\Join\) | \Join | \(\bowtie\) | \bowtie | \(\propto\) | \propto |
| \(\in\) | \in | \(\ni\) | \ni or \owns | \(\vdash\) | \vdash | \(\dashv\) | \dashv |
| \(\models\) | \models | \(\mid\) | \mid | \(\parallel\) | \parallel | \(\perp\) | \perp |
| \(\smile\) | \smile | \(\frown\) | \frown | \(\asymp\) | \asymp | \(:\) | : |
| \(\notin\) | \notin | \(\ne\) | \neq or \ne |
4.2 二元運算符
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \(+\) | + | \(-\) | - | \(\times\) | \times | \(\div\) | \div |
| \(\pm\) | \pm | \(\mp\) | \mp | \(\triangleleft\) | \triangleleft | \(\triangleright\) | \triangleright |
| \(\cdot\) | \cdot | \(\setminus\) | \setminus | \(\star\) | \star | \(\ast\) | \ast |
| \(\cup\) | \cup | \(\cap\) | \cap | \(\sqcup\) | \sqcup | \(\sqcap\) | \sqcap |
| \(\lor\) | \vee or \lor | \(\land\) | \wedge or \land | \(\circ\) | \circ | \(\bullet\) | \bullet |
| \(\oplus\) | \oplus | \(\ominus\) | \ominus | \(\odot\) | \odot | \(\oslash\) | \oslash |
| \(\otimes\) | \otimes | \(\bigcirc\) | \bigcirc | \(\diamond\) | \diamond | \(\uplus\) | \uplus |
| \(\bigtriangleup\) | \bigtriangleup | \(\bigtriangledown\) | \bigtriangledown | \(\lhd\) | \lhd | \(\rhd\) | \rhd |
| \(\unlhd\) | \unlhd | \(\unrhd\) | \unrhd | \(\amalg\) | \amalg | \(\wr\) | \wr |
| \(\dagger\) | \dagger | \(\ddagger\) | \ddagger |
5. 箭頭
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \(\gets\) | \leftarrow or \gets | \(\to\) | \rightarrow or \to | \(\longleftarrow\) | \longleftarrow | \(\longrightarrow\) | \longrightarrow |
| \(\uparrow\) | \uparrow | \(\downarrow\) | \downarrow | \(\updownarrow\) | \updownarrow | \(\leftrightarrow\) | \leftrightarrow |
| \(\Uparrow\) | \Uparrow | \(\Downarrow\) | \Downarrow | \(\Updownarrow\) | \Updownarrow | \(\longleftrightarrow\) | \longleftrightarrow |
| \(\Leftarrow\) | \Leftarrow | \(\Longleftarrow\) | \Longleftarrow | \(\Rightarrow\) | \Rightarrow | \(\Longrightarrow\) | \Longrightarrow |
| \(\Leftrightarrow\) | \Leftrightarrow | \(\Longleftrightarrow\) | \Longleftrightarrow | \(\mapsto\) | \mapsto | \(\longmapsto\) | \longmapsto |
| \(\nearrow\) | \nearrow | \(\searrow\) | \searrow | \(\swarrow\) | \swarrow | \(\nwarrow\) | \nwarrow |
| \(\hookleftarrow\) | \hookleftarrow | \(\hookrightarrow\) | \hookrightarrow | \(\rightleftharpoons\) | \rightleftharpoons | \(\iff\) | \iff |
| \(\leftharpoonup\) | \leftharpoonup | \(\rightharpoonup\) | \rightharpoonup | \(\leftharpoondown\) | \leftharpoondown | \(\rightharpoondown\) | \rightharpoondown |
| \(\leadsto\) | \leadsto |
6. 其他符號
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|---|---|
| \(\dots\) | \dots | \(\cdots\) | \cdots | \(\vdots\) | \vdots | \(\ddots\) | \ddots |
| \(\hbar\) | \hbar | \(\imath\) | \imath | \(\jmath\) | \jmath | \(\ell\) | \ell |
| \(\Re\) | \Re | \(\Im\) | \Im | \(\aleph\) | \aleph | \(\wp\) | \wp |
| \(\forall\) | \forall | \(\exists\) | \exists | \(\mho\) | \mho | \(\partial\) | \partial |
| \(’\) | ’ | \(\prime\) | \prime | \(\emptyset\) | \emptyset | \(\infty\) | \infty |
| \(\nabla\) | \nabla | \(\triangle\) | \triangle | \(\Box\) | \Box | \(\Diamond\) | \Diamond |
| \(\bot\) | \bot | \(\top\) | \top | \(\angle\) | \angle | \(\surd\) | \surd |
| \(\diamondsuit\) | \diamondsuit | \(\heartsuit\) | \heartsuit | \(\clubsuit\) | \clubsuit | \(\spadesuit\) | \spadesuit |
| \(\lnot\) | \neg or \lnot | \(\flat\) | \flat | \(\natural\) | \natural | \(\sharp\) | \sharp |
7.其他
| 符號 | 寫法 | 符號 | 寫法 | 符號 | 寫法 |
|---|---|---|---|---|---|
| \(\\S\) | \S | \(\\P\) | \P |
| 字體 | 寫法 |
|---|---|
| \(\mathbb{R}\) | \mathbb{R} |
| \(mathcal{L}\) | \mathcal{L} |
PS: 原文中還有其他符號（如AMS運算符，希伯來字母等），但MathJax中或是不支持，或是使用頻率太低，故而在這里不再寫入
參考
[2] LaTeX Notes 雷太赫排版系統簡介 v2.56 包太雷
[3] LaTeX數學符號公式匯總