LaTeX 數學公式常用表達式

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LaTeX

1. 括號

• fraction：$\frac{a}{b}$，$\frac{a}{b}$
• parenthesis：$\left( \frac{a}{b} \right)$，$\left( \frac{a}{b} \right)$
• bracket：$\left[ \frac{a}{b} \right]$，$\left[ \frac{a}{b} \right]$
• brace：$\left\{ \frac{a}{b} \right\}$，$\left\{ \frac{a}{b} \right\}$
• absolute value：$\left| \frac{a}{b} \right|$，$\left| \frac{a}{b} \right|$
• angle bracket：$\left \langle \frac{a}{b} \right \rangle$，$\left \langle \frac{a}{b} \right \rangle$
• norm（範數）：$\left \| \frac{a}{b} \right \|$，$\left \| \frac{a}{b} \right \|$
• floor function（取整函數）：$\left \lfloor \frac{a}{b} \right \rfloor$，$\left \lfloor \frac{a}{b} \right \rfloor$
• ceiling function（取頂函數）：$\left \lceil \frac{c}{d} \right \rceil$，$\left \lceil \frac{c}{d} \right \rceil$
• slashes and backslashes：$\left / \frac{a}{b} \right \backslash$，$\left / \frac{a}{b} \right \backslash$
• arrows：
  • $\left \uparrow \frac{a}{b} \right \downarrow$，$\left \uparrow \frac{a}{b} \right \downarrow$
  • $\left \Uparrow \frac{a}{b} \right \Downarrow$，$\left \Uparrow \frac{a}{b} \right \Downarrow$
  • $\left \updownarrow \frac{a}{b} \right \Updownarrow$，$\left \updownarrow \frac{a}{b} \right \Updownarrow$
• mixed brackets：$\left [ 0,1 \right )\left \langle \psi \right |$，$\left [ 0,1 \right )\left \langle \psi \right |$
• single left parenthesis：$\left \{ \frac{a}{b} \right .$，$\left \{ \frac{a}{b} \right .$
• single right parenthesis：$\left . \frac{a}{b} \right \}$，$\left . \frac{a}{b} \right \}$
• size of parenthesis（\big < \Big < \bigg < \Bigg）：$\Bigg ( \bigg [ \Big \{ \big \langle \left | \| x \| \right | \big \rangle \Big \} \bigg ] \Bigg )$，$\Bigg ( \bigg [ \Big \{ \big \langle \left | \| x \| \right | \big \rangle \Big \} \bigg ] \Bigg )$

2. 上下標

• superscript：$a^{b+c}$，$a^{b+c}$
• subscript：$a_{b+c}$，$a_{b+c}$
• note：$a^{n}_{m}$, $a_{m}^{n}$, ${a^{n}}_{m}$, ${a_{m}}^{n}$，$a^{n}_{m}$, $a_{m}^{n}$, ${a^{n}}_{m}$, ${a_{m}}^{n}$
• derivative：$a=a'$, $b_{0}'=b_{0'}$, $c'^{2}=(c')^{2}$，$a=a'$, $b_{0}'=b_{0'}$, $c'^{2}=(c')^{2}$
• others：$\overset{*}{X}$, $\underset{\dag}{A}$, $\underset{\dag}{\overset{*}{X}}$，$\overset{*}{X}$, $\underset{\dag}{A}$, $\underset{\dag}{\overset{*}{X}}$

3. 矩陣

$\begin{gathered} \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \quad \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} \quad \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} \quad \begin{Bmatrix} 1 & 0 \\ 0 & -1 \end{Bmatrix} \quad \begin{vmatrix} a & b \\ c & d \end{vmatrix} \quad \begin{Vmatrix} i & 0 \\ 0 & -i \end{Vmatrix} \end{gathered}$

$$
\begin{gathered}
\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}
\quad
\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}
\quad
\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}
\quad
\begin{Bmatrix} 1 & 0 \\ 0 & -1 \end{Bmatrix}
\quad
\begin{vmatrix} a & b \\ c & d \end{vmatrix}
\quad
\begin{Vmatrix} i & 0 \\ 0 & -i \end{Vmatrix}
\end{gathered}
$$

4. 方程組

$\left\{ \begin{array}{lr} x=\dfrac{3\pi}{2}(1+2t)\cos(\dfrac{3\pi}{2}(1+2t)), & \\ y=s, & 0\leq s\leq L,|t|\leq1.\\ z=\dfrac{3\pi}{2}(1+2t)\sin(\dfrac{3\pi}{2}(1+2t)), & \end{array} \right.$

$$
\left\{  
             \begin{array}{lr}  
             x=\dfrac{3\pi}{2}(1+2t)\cos(\dfrac{3\pi}{2}(1+2t)), &  \\  
             y=s, & 0\leq s\leq L,|t|\leq1.\\  
             z=\dfrac{3\pi}{2}(1+2t)\sin(\dfrac{3\pi}{2}(1+2t)), &    
             \end{array}  
\right.
$$

$\left\{ \begin{array}{rcl} IF_{k}(\hat{t}_{k,m})=IF_{m}(\hat{t}_{k,m}), & \\ IF_{k}(\hat{t}_{k,m}) \pm h= IF_{m}(\hat{t}_{k,m}) \pm h , &\\ \left |IF'_{k}(\hat{t}_{k,m} - IF'_{m}(\hat{t}_{k,m} \right |\geq d , & \end{array} \right.$

$$
\left\{  
\begin{array}{rcl}
    IF_{k}(\hat{t}_{k,m})=IF_{m}(\hat{t}_{k,m}), & \\
    IF_{k}(\hat{t}_{k,m}) \pm h= IF_{m}(\hat{t}_{k,m}) \pm h  , &\\
    \left |IF'_{k}(\hat{t}_{k,m} - IF'_{m}(\hat{t}_{k,m} \right |\geq d , &   
\end{array}
\right.  
$$ 

5. 分段函數

$f(x)=\left\{ \begin{aligned} x & = & \cos(t) \\ y & = & \sin(t) \\ z & = & \frac xy \end{aligned} \right.$

$$ 
f(x)=\left\{
\begin{aligned}
x & = & \cos(t) \\
y & = & \sin(t) \\
z & = & \frac xy
\end{aligned}
\right.
$$

$F^{HLLC}=\left\{ \begin{array}{rcl} F_L & & {0 < S_L}\\ F^*_L & & {S_L \leq 0 < S_M}\\ F^*_R & & {S_M \leq 0 < S_R}\\ F_R & & {S_R \leq 0} \end{array} \right.$

$$ 
F^{HLLC}=\left\{
\begin{array}{rcl}
F_L       &      & {0      <      S_L}\\
F^*_L     &      & {S_L \leq 0 < S_M}\\
F^*_R     &      & {S_M \leq 0 < S_R}\\
F_R       &      & {S_R \leq 0}
\end{array} \right. 
$$

$f(x)= \begin{cases} 0& \text{x=0}\\ 1& \text{x!=0} \end{cases}$

$$
f(x)=
\begin{cases}
0& \text{x=0}\\
1& \text{x!=0}
\end{cases}
$$

6. 其他

• space：$a\quad b$，\quad
• $90^{\circ}$，$90^{\circ}$
• infinite：$\infty$，$\infty$
• sigma：$\sum_{i=1}^{n}a_{i}$，$\sum_{i=1}^{n}a_{i}$
• capital pi：$\prod_{i=1}^{n}b_{i}$，$\prod_{i=1}^{n}b_{i}$
• definite integral：$\int_{a}^{b}f(x)$，$\int_{a}^{b}f(x)$
• limit：$\lim_{n\rightarrow\infty}a_{n}$，$\lim_{n\rightarrow\infty}a_{n}$

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原文鏈接：https://qwert.blog.csdn.net/article/details/105898707