LaTeX｜1-零零碎碎

约 745 个字 151 行代码预计阅读时间 4 分钟

向量篇 | 矩阵篇 | 行列式篇：⚓︎

入门通用进阶行列式矩阵画表格

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

\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}

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

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

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

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

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

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

\[
\def\arraystretch{2}
\begin{array}{c:c|c}
    a & \beta + \gamma & c \cr \hline
    d & e & f \cr
    \hdashline
    g & h & i
\end{array}
\]

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

LaTeX 希腊字母篇

\[\def\arraystretch{2}
   \begin{array}{|c|c|c|c|c|}
   \hline
   \hline
   \text{原型} & 符号 &   \text{var} + 原型 & 首字母大写 & \text{var} + 首字母大写 \cr \hline
   \text{alpha} &\alpha   &     &           \Alpha   &  A     \cr \hline    
\text{beta}  & \beta &           &         \Beta &       B           \cr \hline
\text{gamma}  & \gamma &       &            \Gamma &      \varGamma   \cr \hline
\text{delta}  & \delta &        &           \Delta &      \varDelta   \cr \hline
\text{epsilon}  & \epsilon &    \varepsilon &   \Epsilon  &  E          \cr \hline
\text{zeta}  & \zeta &           &         \Zeta &       Z           \cr \hline
\text{eta}  & \eta &              &       \Eta &        E           \cr \hline
\text{theta}  & \theta &      \vartheta &     \Theta    &  \varTheta  \cr \hline
\text{iota}  & \iota &         &           \Iota &       I           \cr \hline
\text{kappa}  & \kappa &      \varkappa &     \Kappa   &   K          \cr \hline
\text{lambda}  & \lambda &     &             \Lambda &     \varLambda  \cr \hline
\text{mu}  & \mu &              &        \Mu &         M           \cr \hline
\text{nu}  & \nu &               &       \Nu &         N           \cr \hline
\text{xi}  & \xi &                &      \Xi &         \varXi      \cr \hline
\text{原型} & 符号 &   \text{var} + 原型 & 首字母大写 & \text{var} + 首字母大写 \cr \hline
\text{omicron}  & \omicron &       &          \Omicron &    O           \cr \hline
\text{pi}  & \pi &         \varpi &        \Pi    &     \varPi     \cr \hline
\text{rho}  & \rho &        \varrho &       \Rho    &    P          \cr \hline
\text{sigma}  & \sigma &      \varsigma &     \Sigma    &  \varSigma  \cr \hline
\text{tau}  & \tau &                   &  \Tau &        T           \cr \hline
\text{upsilon}  & \upsilon &            &     \Upsilon &    \varUpsilon \cr \hline
\text{phi}  & \phi &        \varphi &    \Phi&        \varPhi    \cr \hline
\text{chi}  & \chi &            &         \Chi &        X           \cr \hline
\text{psi}  & \psi &             &        \Psi &        \varPsi     \cr \hline
\text{omega}  & \omega &          &         \Omega &      \varOmega   \cr \hline
\hline
\end{array}\]

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

$\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathbf{abcdefghijklmnopqrstuvwxyz}$

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

\mathit{ }⚓︎

斜体数字

$\mathit{1234567890 ABCDE abcdef}$

\(\mathit{1234567890 ABCDE abcdef}\)

\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

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

$\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathscr{ 1234567890}$

\mathfrak{ }⚓︎

哥特式字体

\(\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)

\(\mathfrak{1234567890}\)

\(\mathfrak{abcdefghijklmnopqrstuvwxyz}\)

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

\mathtt{ }⚓︎

等宽字体

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

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

杂七杂八⚓︎

大括号在min/max的正下方打出下标累乘符号在求和符号正上方和正下方加字母求和符号下重叠

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

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

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

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

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

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

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

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

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

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

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

在箭头正上方和正下方加字符约束条件的大括号🌊 波浪号 | 上波浪 | 对于任意另一种大括号

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

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

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

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

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

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

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

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

偏导符号积分符号范式符号梯度符号加注释实数加方框上 / 下总括号

\[\partial y\]

$$ \partial y $$

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

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

\[\Vert x - y \Vert\]

$$ \Vert x - y \Vert $$

\[\nabla\]

$$ \nabla $$

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

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

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

$$\Re \real \reals \Reals \Z$$

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

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

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

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

表示均值的那个拔：bar表示回归中的期望值的：hat粗体

\[\bar{A}\]

$$\bar{A}$$

\[\hat{A}\]

$$\hat{A}$$

\[\textbf{\alpha}\]

$$\textbf{\alpha}$$

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


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


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

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