latex公式：列向量、矩阵、方程组

2024-02-25 14:33| 来源: 网络整理| 查看: 265

注释多个公式并列

T F − I D F = T F ∗ I D F = N 文本总的单词个数 ∗ l o g 2 ( 文本总数包含这个单词的文本数量 ) \begin{aligned} TF-IDF &=TF*IDF \\ &= \frac{N}{文本总的单词个数}*log_2(\frac{文本总数}{包含这个单词的文本数量}) \end{aligned} TF−IDF=TF∗IDF=文本总的单词个数N∗log2(包含这个单词的文本数量文本总数)

$$ \begin{aligned} TF-IDF &=TF*IDF \\ &= \frac{N}{文本总的单词个数}*log_2(\frac{文本总数}{包含这个单词的文本数量}) \end{aligned} $$ 花括号

a + b + ⋯ ⏞ = t + z ⏟ total a + b + ⋯ ⏞ 126 + z \begin{aligned} \underbrace{a + \overbrace{b+\cdots}^{=t}+z}_{\text{total}} ~~ a + {\overbrace{b+\cdots}}^{126}+z \end{aligned} total a+b+⋯ =t+z a+b+⋯ 126+z 代码：

\begin{aligned} \underbrace{a + \overbrace{b+\cdots}^{=t}+z}_{\text{total}} ~~ a + {\overbrace{b+\cdots}}^{126}+z \end{aligned}

m { a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋯ ⋱ ⋮ a m 1 a m 2 ⋯ a m n ⏞ n m\left\{\overbrace{ \begin{array} {cccc} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\cdots&\ddots&\vdots&\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\ \end{array} }^{n} \right. m⎩⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎧a11a21⋮am1a12a22⋯am2⋯⋯⋱⋯a1na2n⋮amn n

代码：

m\left\{\overbrace{ \begin{array} {cccc} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\cdots&\ddots&\vdots&\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\ \end{array} }^{n} \right.

R m ∗ n m = 9947 ∗ n = 15774 = a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋯ ⋱ ⋮ a m 1 a m 2 ⋯ a m n \mathbb{R}^{m*n_{m=9947*n=15774}}=\begin{array} {cccc} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\cdots&\ddots&\vdots&\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\ \end{array} Rm∗nm=9947∗n=15774=a11a21⋮am1a12a22⋯am2⋯⋯⋱⋯a1na2n⋮amn 代码：

\mathbb{R}^{m*n_{m=9947*n=15774}}=\begin{array} {cccc} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\cdots&\ddots&\vdots&\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\ \end{array} 矩阵字母表示，双R表示 $\mathbb{R}^{9947*15774}$

R 9947 ∗ 15774 \mathbb{R}^{9947*15774} R9947∗15774

分数公式

T F = 1 2 TF=\frac{1}{2} TF=21

$$ TF=\frac{1}{2} $$

通过\frac来实现

矩阵

m { a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋯ ⋱ ⋮ a m 1 a m 2 ⋯ a m n ⏞ n \begin{aligned} m\left\{\overbrace{ \begin{array} {cccc} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\cdots&\ddots&\vdots&\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\ \end{array} }^{n} \right. \end{aligned} m⎩⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎧a11a21⋮am1a12a22⋯am2⋯⋯⋱⋯a1na2n⋮amn n 代码：

\begin{aligned} m\left\{\overbrace{ \begin{array} {cccc} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\cdots&\ddots&\vdots&\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\ \end{array} }^{n} \right. \end{aligned}

R m ∗ n = a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋯ ⋱ ⋮ a m 1 a m 2 ⋯ a m n \begin{aligned} \mathbb{R}^{m*n}=\begin{array} {|cccc|} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\cdots&\ddots&\vdots&\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\ \end{array} \end{aligned} Rm∗n=a11a21⋮am1a12a22⋯am2⋯⋯⋱⋯a1na2n⋮amn

代码：

\begin{aligned} \mathbb{R}^{m*n}=\begin{array} {|cccc|} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\cdots&\ddots&\vdots&\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\ \end{array} \end{aligned} 向量

y = y 1 y 2 ⋮ y n \begin{aligned} y= \begin{array} {|c|} y_{1} \\ y_{2}\\ \vdots&\\ y_{n} \end{array} \end{aligned} y=y1y2⋮yn

源码如下：

$$ \begin{aligned} y= \begin{array} {|c|} y_{1} \\ y_{2}\\ \vdots&\\ y_{n} \end{array} \end{aligned} $$ 方程组

{ w + b = 3 2 w + b = 8 \left\{ \begin{array}{l} w+b=3 \\ 2w+b=8 \end{array} \right. {w+b=32w+b=8

latex 公式为：

$$ \left\{ \begin{array}{l} w+b=3 \\ 2w+b=8 \end{array} \right. $$ 表格

这其实是markdown的表格格式，比latex要简单一些

字段名称类型描述说明content_idInt数据ID/contentString文本内容/subjectString主题提取或依据上下文归纳出来的主题sentiment_valueInt情感分析分析出的情感sentiment_wordString情感词情感词 | 字段名称 | 类型 | 描述 | 说明 | |-----------------|--------|----------|--------------------------------| | content_id | Int | 数据ID | / | | content | String | 文本内容 | / | | subject | String | 主题 | 提取或依据上下文归纳出来的主题 | | sentiment_value | Int | 情感分析 | 分析出的情感 | | sentiment_word | String | 情感词 | 情感词 | 字母下边有下标

max ⁡ a < x < b \max \limits_{a

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