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LaTeX｜1-零零碎碎

约 734 个字 156 行代码 预计阅读时间 4 分钟

向量篇 | 矩阵篇 | 行列式篇 ：⚓︎

事实上已经有非常多人做过这个了，这里记录一些我反复查阅过的内容。

Some excellent links: - LaTeX-Math速查手册 by Emory Huang

\(\begin{pmatrix} a_1 \\ a_2 \end{pmatrix}\)

\begin{pmatrix}

a_1 \\ a_2

\end{pmatrix}

\(\begin{pmatrix} a_1 & a_2 \\ a_3 & a_4\end{pmatrix}\)

\begin{pmatrix} 
a_1 & a_2 \\ 
a_3 & a_4
\end{pmatrix}

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

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

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

\[
\def\arraystretch{2}
\begin{array}{c:c|c}
    a & \beta + \gamma & c \cr \hline
    d & e & f \cr
    \hdashline
    g & h & i
\end{array}
\]
$$
\def\arraystretch{2}
\begin{array}{c:c|c}
    a & \beta + \gamma & c \cr \hline
    d & e & f \cr
    \hdashline
    g & h & i
\end{array}
% 这里是缩进敏感的
$$

集合操作与基础符号⚓︎

拼写 展示 拼写 展示 拼写 展示 拼写 展示
\geq \(\geq\) \leq \(\leq\) \neq \(\neq\) \forall \(\forall\)
\cup \(\cup\) \cap \(\cap\) \land \(\land\) \lor \(\lor\)
\neg \(\neg\) A \setminus B \(A \setminus B\) \emptyset \(\emptyset\) \subset \(\subset\)
\mid \(\mid\) A \subsetneq B \(A \subsetneq B\) \exist \(\exist\) \And \(\And\)
\because \(\because\) \therefore \(\therefore\) \bar{t} \(\bar{t}\) \bot \(\bot\)

希腊字母⚓︎

拼写 展示 拼写 展示 拼写 展示 拼写 展示
\alpha \(\alpha\) \rho \(\rho\) \iota \(\iota\) \Delta \(\Delta\)
\beta \(\beta\) \sigma \(\sigma\) \kappa \(\kappa\) \Theta \(\Theta\)
\gamma \(\gamma\) \varsigma \(\varsigma\) \lambda \(\lambda\) \Lambda \(\Lambda\)
\delta \(\delta\) \tau \(\tau\) \mu \(\mu\) \Xi \(\Xi\)
\epsilon \(\epsilon\) \upsilon \(\upsilon\) \mu \(\mu\) \Sigma \(\Sigma\)
\zeta \(\zeta\) \chi \(\chi\) \nu \(\nu\) \Upsilon \(\Upsilon\)
\eta \(\eta\) \psi \(\psi\) \xi \(\xi\) \Phi \(\Phi\)
\theta \(\theta\) \omega \(\omega\) \pi \(\pi\) \Psi \(\Psi\)
\vartheta \(\vartheta\) \Gamma \(\Gamma\) \Omega \(\Omega\) \varOmega \(\varOmega\)
\varPsi \(\varPsi\) \varPhi \(\varPhi\) \Pi \(\Pi\) \varepsilon \(\varepsilon\)

奇异字母与英文字体⚓︎

\mathbb{ }⚓︎

  • Black Board Bold 一般用于表示数学和物理学中的向量或集合的符号
$\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathbb{abcdefghijklmnopqrstuvwxyz}$

\(\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\) \(\mathbb{abcdefghijklmnopqrstuvwxyz}\) \(\mathbb{1234}\)

\mathbf{ }⚓︎

  • 正粗体
$\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathbf{abcdefghijklmnopqrstuvwxyz}$
$\mathbf{0123456789}$

\(\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\) \(\mathbf{abcdefghijklmnopqrstuvwxyz}\) \(\mathbf{0123456789}\)

\mathit{ }⚓︎

  • 斜体数字
$\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathit{abcdefghijklmnopqrstuvwxyz}$
$\mathit{0123456789}$

\(\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\) \(\mathit{abcdefghijklmnopqrstuvwxyz}\) \(\mathit{0123456789}\)

\mathcal{ }⚓︎

  • 书法字体（仅限大写），用于方案识别，密码学概念；

$\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
\(\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)

\mathscr{ }⚓︎

  • 花体字，常用大写。
$\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathscr{abcdefghijklmnopqrstuvwxyz}$
$\mathscr{ 1234567890}$

\(\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\) \(\mathscr{abcdefghijklmnopqrstuvwxyz}\) \(\mathscr{ 1234567890}\)

\mathfrak{ }⚓︎

  • 哥特式字体

\(\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)

\(\mathfrak{1234567890}\)

\(\mathfrak{abcdefghijklmnopqrstuvwxyz}\)

$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathfrak{1234567890}$
$\mathfrak{abcdefghijklmnopqrstuvwxyz}$

\mathtt{ }⚓︎

  • 等宽字体

\(\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\) \(\mathtt{abcdefghijklmnopqrstuvwxyz}\) \(\mathtt{ 1234567890}\)

$\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathtt{abcdefghijklmnopqrstuvwxyz}$
$\mathtt{ 1234567890}$

杂七杂八⚓︎

\[\mathop{\max} \left\{ \frac{pV}{nrT} \right\}\]
$$\mathop{\max} \left\{ \frac{pV}{nrT} \right\}$$

\[\mathop{\arg\min}\limits_{\theta} \hspace{8pt} \mathop{\min}\limits_{\theta}\]
$\mathop{\arg\min}\limits_{\theta}$

$\mathop{\min}\limits_{\theta}$

\[\prod \limits_{i=0}^n\]
$\prod \limits_{i=0}^n$

\[\sum \limits_{i=1}^{n}\]
$\sum \limits_{i=1}^{n}$

\[\sum_{\substack{0<i<m\cr 0<j<n}}\]
$\sum_{\substack{0<i<m\cr 0<j<n}}$

\[A\stackrel{r/c/}{\rightarrow}B\]
$A\stackrel{r/c/}{\rightarrow}B$

\[s.t \hspace{4pt} \left\{ \begin{aligned} \sum \limits^{n}_{j=1} x_{ij} \leq a_i , i = 1,2,..,m \\ \sum \limits^{n}_{i=1} x_{ij} = b_j , j = 1,2,..,n     \end{aligned}  \right. \]
$$
s.t. 
\hspace{4pt} 
\left\{ 
\begin{aligned} \sum \limits^{n}_{j=1} x_{ij} \leq a_i , i = 1,2,..,m \\
\sum \limits^{n}_{i=1} x_{ij} = b_j , j = 1,2,..,n 
\end{aligned} 
\right. 
$$

\[\sim  \hspace{10pt}  \tilde{A}  \hspace{10pt} \forall\]
$$ \sim  \hspace{10pt}  \tilde{A}  \hspace{10pt} \forall$$

\[f(n)=\begin{dcases} 1 & n = 1 \cr \sum_{i=1}^{n-1} f(i) & \text{Otherwise.}\end{dcases}\]
$$f(n)=\begin{dcases} 1 & n = 1 \cr \sum_{i=1}^{n-1} f(i) & \text{Otherwise.}\end{dcases}$$

\[\partial y\]
$$ \partial y $$

\[\int \limits^{a}_{b}\]
$$\int \limits^{a}_{b}$$

\[\Vert x - y \Vert\]
$$ \Vert x - y \Vert $$

\[\nabla\]
$$ \nabla $$

\[\tag{2.1}E = mc^2\]
$$\tag{(2.1)}E = mc^2$$

\[\Re \hspace{4pt} \real \hspace{4pt}  \reals \hspace{4pt}  \Reals \hspace{4pt}  \Z\]
$$\Re \real \reals \Reals \Z$$

\[\boxed{\pi=\dfrac{c}{d}}\]
$$\boxed{\pi=\dfrac{c}{d}}$$

\[\overbrace{x+⋯+x}^{n\text{ times}} \hspace{6pt} \underbrace{x+⋯+x}_{n\text{ times}}\]
$$\overbrace{x+⋯+x}^{n\text{ times}} \hspace{6pt} \underbrace{x+⋯+x}_{n\text{ times}}$$

\[\bar{A}\]
$$\bar{A}$$

\[\hat{A}\]
$$\hat{A}$$

\[\textbf{\alpha}\]
$$\textbf{\alpha}$$

$$\text{价格}  \hspace{90pt} \text{容积} \hspace{90pt}  \text{美观} \hspace{50cm} \\[2ex]  B_{1}^{(3)} = \begin{pmatrix}
     1 & 1/5 & 1/8 \\ 
      5 & 1 & 1/4 \\ 
    8 & 4 & 1
    \end{pmatrix} \hspace{5pt} 
 B_{5}^{(3)} = \begin{pmatrix}
     1 & 6 & 4 \\ 
      1/6 & 1 & 1/3 \\ 
    1/4 & 3 & 1
    \end{pmatrix} \hspace{5pt} 
    B_{9}^{(3)} = \begin{pmatrix}
     1 & 1/7 & 3 \\ 
      7 & 1 & 9 \\ 
    1/3 & 1/9 & 1
    \end{pmatrix} \hspace{20cm}$$


$$\text{冷冻}  \hspace{90pt} \text{功率} \hspace{90pt} \text{体积} \hspace{50cm}\\[2ex] B_{2}^{(3)} = \begin{pmatrix}
     1 & 2 & 9 \\ 
      1/2 & 1 & 7 \\ 
    1/9 & 1/7 & 1
    \end{pmatrix} \hspace{5pt} 
B_{6}^{(3)} = \begin{pmatrix}
     1 & 1/8 & 1/4 \\ 
      8 & 1 & 5 \\ 
    4 & 1/5 & 1
    \end{pmatrix}\hspace{5pt} 
B_{10}^{(3)} = \begin{pmatrix}
     1 & 1/7 & 1/2 \\ 
      7 & 1 & 4 \\ 
    2 & 1/4 & 1
    \end{pmatrix} \hspace{50cm}$$


$$\text{快速}  \hspace{90pt} \text{分贝} \hspace{90pt} \text{售后} \hspace{50cm}\\[2ex]  B_{3}^{(3)} = \begin{pmatrix} 
 1 & 5 & 7 \\ 
 1/5 & 1 & 3 \\
 1/7 & 1/3 & 1 
 \end{pmatrix} \hspace{5pt}
B_{7}^{(3)} = \begin{pmatrix} 
  1 & 5 & 8 \\ 
  1/5 & 1 & 4 \\ 
  1/8 & 1/4 & 1 \end{pmatrix}\hspace{5pt}
B_{11}^{(3)} = \begin{pmatrix}
1 & 3 & 9 \\
 1/3 & 1 & 5 \\ 
1/9 & 1/5 & 1
\end{pmatrix} \hspace{50cm}$$

$$\text{制热} \hspace{90pt}  \text{清洗} \hspace{50cm}  \\[2ex]  B_{4}^{(3)} = \begin{pmatrix}
     1 & 1/5 & 4 \\ 
      5 & 1 & 8 \\ 
    1/4 & 1/8 & 1
    \end{pmatrix} \hspace{5pt} 
B_{8}^{(3)} = \begin{pmatrix}
     1 & 4 & 1/5 \\ 
      1/4 & 1 & 1/8 \\ 
    5 & 8 & 1
    \end{pmatrix}\hspace{50cm}$$