LaTex 希腊字母、数学符号、公式换行

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#Latex数学符号

于 2022-05-09 10:39:27 首次发布

Latex数学符号专栏收录该内容

1 篇文章

订阅专栏

本文详细介绍了LaTeX中常用的希腊字母、数学字体样式、公式换行与对齐方法，并通过实例展示了如何表示样本集、损失函数、高斯分布以及优化问题。此外，还提供了完整符号的使用示例，对于理解和编写复杂的数学公式极具参考价值。

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1.常用希腊字母

2.特殊样式

数学特殊字体样式 \mathbb， \mathsf， \mathtt, \mathit，\mathcal

\mathbb：blackboard bold，板粗体

\mathcal：calligraphy，美术字

\mathrm：math roman，罗马字体

\mathbf：math boldfac，黑体

\mathcal ，花体

\mathcal D 表示样本集，

\mathcal L 表示loss 函数，

\mathcal N 表示高斯分布函数

\boldsymbol 希腊字母加黑体，如果采用\mathbf则不起作用

a) \mathbb{R},\mathsf{R},\mathtt{R}, \mathit{R},\mathcal{R}

\mathbb{N},\mathsf{N},\mathtt{N}, \mathit{N},\mathcal{N} #对应效果如下

$\mathbb{R},\mathsf{R},\mathtt{R}, \mathit{R},\mathcal{R}$ ,

$\mathbb{N},\mathsf{N},\mathtt{N}, \mathit{N},\mathcal{N}$

b) L_{exp}(H)=\mathbb{E}_{x\sim D}[e^{-f(x)H(x)}] #对应效果如下

$L_{exp}(H)=\mathbb{E}_{x\sim D}[e^{-f(x)H(x)}]$

c) x\sim\mathcal N(\mu,\sigma^2) #对应效果如下

$x\sim\mathcal N(\mu,\sigma^2)$

d) \mathop{\arg\min}\limits_{\theta}, \mathop{\arg\min}\limits_{\theta}

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

3. 公式换行、对齐及序号位置

\begin{align}

f(w,z) &= \left \| x - zw \right \|^2 \nonumber \\

& = (x- zw)^T(x - zw) \nonumber \\

& = (x ^{T}x-2zw ^{T}x +w^Tz^Tzw) \nonumber

\end{align}

$\begin{align} f(w,z) &= \left \| x - zw \right \|^2 \nonumber \\ & = (x- zw)^T(x - zw) \nonumber \\ & = (x ^{T}x-2zw ^{T}x +w^Tz^Tzw) \nonumber \end{align}$

\begin{align}

f(w,z) &= \left \| x - zw \right \|^2 \nonumber \\

& = (x- zw)^T(x - zw) \nonumber \\

& = (x ^{T}x-2zw ^{T}x +w^Tz^Tzw)

\end{align}

$\begin{align} f(w,z) &= \left \| x - zw \right \|^2 \nonumber \\ & = (x- zw)^T(x - zw) \nonumber \\ & = (x ^{T}x-2zw ^{T}x +w^Tz^Tzw) \end{align}$

\begin{align}

\nabla\hat{p}(X^{(t)})\equiv g({X^{(t)}})&=\frac{2}{Nh^{d+2}}\bigg(\frac{1}{2\pi}\bigg)^{(d/2)}\sum_{i=1}^N \bigg(X^{(t)}-X_{i}\bigg)K^\prime\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg) \nonumber \\

&=\frac{1}{Nh^{d+2}}\bigg(\frac{1}{2\pi}\bigg)^{(d/2)}\sum_{i=1}^N \bigg(X_{i}- X^{(t)}\bigg)K\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg) \nonumber \\

&=\frac{1}{Nh^{d+2}}\bigg(\frac{1}{2\pi}\bigg)^{(d/2)}\bigg[\sum_{i=1}^N K\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg)\bigg]\bigg[\frac{\sum_{i=1}^NK\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg)X_i}{\sum_{i=1}^NK\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg)}-X^{(t)}\bigg] \ (1.1) \nonumber

\end{align}

$\begin{align} \nabla\hat{p}(X^{(t)})\equiv g({X^{(t)}})&=\frac{2}{Nh^{d+2}}\bigg(\frac{1}{2\pi}\bigg)^{(d/2)}\sum_{i=1}^N \bigg(X^{(t)}-X_{i}\bigg)K^\prime\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg) \nonumber \\ &=\frac{1}{Nh^{d+2}}\bigg(\frac{1}{2\pi}\bigg)^{(d/2)}\sum_{i=1}^N \bigg(X_{i}- X^{(t)}\bigg)K\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg) \nonumber \\ &=\frac{1}{Nh^{d+2}}\bigg(\frac{1}{2\pi}\bigg)^{(d/2)}\bigg[\sum_{i=1}^N K\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg)\bigg]\bigg[\frac{\sum_{i=1}^NK\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg)X_i}{\sum_{i=1}^NK\bigg(\bigg|\bigg|\frac{X^{(t)}-X_i}{h}\bigg|\bigg|^2\bigg)}-X^{(t)}\bigg] \ (1.1) \nonumber \end{align}$