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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

(a1a2)\begin{pmatrix} a_1 \\ a_2 \end{pmatrix}

\begin{pmatrix}

a_1 \\ a_2

\end{pmatrix}

(a1a2a3a4)\begin{pmatrix} a_1 & a_2 \\ a_3 & a_4\end{pmatrix}

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

(a11⋯a1n⋮⋱⋮an1⋯ann)
\begin{pmatrix}
 a_{11} & \cdots & a_{1n} \\ 
  \vdots & \ddots & \vdots \\ 
  a_{n1} & \cdots & a_{nn}  
\end{pmatrix}

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

∣a11⋯a1n⋮⋱⋮an1⋯ann∣
\begin{vmatrix}
 a_{11} & \cdots & a_{1n} \\ 
  \vdots & \ddots & \vdots \\ 
  a_{n1} & \cdots & a_{nn}  
\end{vmatrix}

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

[a11⋯a1n⋮⋱⋮an1⋯ann]
\begin{bmatrix}
 a_{11} & \cdots & a_{1n} \\ 
  \vdots & \ddots & \vdots \\ 
  a_{n1} & \cdots & a_{nn}  
\end{bmatrix}

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

aβ+γcdefghi
\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∖BA \setminus B \emptyset ∅\emptyset \subset ⊂\subset
\mid ∣\mid A \subsetneq B A⊊BA \subsetneq B \exist ∃\exist \And &\And
\because ∵\because \therefore ∴\therefore \bar{t} tˉ\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 α\alpha \rho ρ\rho \iota ι\iota \Delta Δ\Delta
\beta β\beta \sigma σ\sigma \kappa κ\kappa \Theta Θ\Theta
\gamma γ\gamma \varsigma ς\varsigma \lambda λ\lambda \Lambda Λ\Lambda
\delta δ\delta \tau τ\tau \mu μ\mu \Xi Ξ\Xi
\epsilon ϵ\epsilon \upsilon υ\upsilon \mu μ\mu \Sigma Σ\Sigma
\zeta ζ\zeta \chi χ\chi \nu ν\nu \Upsilon Υ\Upsilon
\eta η\eta \psi ψ\psi \xi ξ\xi \Phi Φ\Phi
\theta θ\theta \omega ω\omega \pi π\pi \Psi Ψ\Psi
\vartheta ϑ\vartheta \Gamma Γ\Gamma \Omega Ω\Omega \varOmega Ω\varOmega
\varPsi Ψ\varPsi \varPhi Φ\varPhi \Pi Π\Pi \varepsilon ε\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
$\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathbb{abcdefghijklmnopqrstuvwxyz}$

ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ} abcdefghijklmnopqrstuvwxyz\mathbb{abcdefghijklmnopqrstuvwxyz} 1234\mathbb{1234}

\mathbf{ }⚓︎

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

ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ} abcdefghijklmnopqrstuvwxyz\mathbf{abcdefghijklmnopqrstuvwxyz} 0123456789\mathbf{0123456789}

\mathit{ }⚓︎

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

ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ} abcdefghijklmnopqrstuvwxyz\mathit{abcdefghijklmnopqrstuvwxyz} 0123456789\mathit{0123456789}

\mathcal{ }⚓︎

  • 书法字体（仅限大写），用于方案识别，密码学概念；

$\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

\mathscr{ }⚓︎

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

ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ} abcdefghijklmnopqrstuvwxyz\mathscr{abcdefghijklmnopqrstuvwxyz} 1234567890\mathscr{ 1234567890}

\mathfrak{ }⚓︎

  • 哥特式字体

ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

1234567890\mathfrak{1234567890}

abcdefghijklmnopqrstuvwxyz\mathfrak{abcdefghijklmnopqrstuvwxyz}

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

\mathtt{ }⚓︎

  • 等宽字体

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

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

杂七杂八⚓︎

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

arg⁡min⁡θmin⁡θ\mathop{\arg\min}\limits_{\theta} \hspace{8pt} \mathop{\min}\limits_{\theta}
$\mathop{\arg\min}\limits_{\theta}$

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

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

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

∑0<i<m0<j<n\sum_{\substack{0<i<m\cr 0<j<n}}
$\sum_{\substack{0<i<m\cr 0<j<n}}$

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

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

∼A~∀\sim  \hspace{10pt}  \tilde{A}  \hspace{10pt} \forall
$$ \sim  \hspace{10pt}  \tilde{A}  \hspace{10pt} \forall$$

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

∂y\partial y
$$ \partial y $$

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

∥x−y∥\Vert x - y \Vert
$$ \Vert x - y \Vert $$

∇\nabla
$$ \nabla $$

E=mc2(2.1)\tag{2.1}E = mc^2
$$\tag{(2.1)}E = mc^2$$

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

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

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

Aˉ\bar{A}
$$\bar{A}$$

A^\hat{A}
$$\hat{A}$$



$$\textbf{\alpha}$$









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


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


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

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