LaTex数学公式
排版方式:
行级元素(inline)：使用$...$，表示公式的首尾
块级元素(displayed)：使用$$...$$，默认居中显示
LaTex数学符号表
小写希腊字母
大写希腊字母
数学函数名
二元关系符
二元运算符
大尺寸运算符
箭头
定界符
大尺寸定界符
其它符号
AMS二元关系符
AMS二元否定关系符和箭头
举例：
$$
x_i^2
$$
\[x_i^2
\]
$$
\log_2 x
$$
\[\log_2 x
\]
$$
10^{10}
$$
\[10^{10}
\]
$$
\{1+2\}
$$
\[ \{1+2\}
\]
$$
\frac{1+1}{2}+1
$$
\[\frac{1+1}{2}+1
\]
$$
\sum_1^n
$$
\[\sum_1^n
\]
$$
\int_1^n
$$
\[\int_1^n
\]
$$
lim_{x\to\infty}
$$
\[lim_{x\to\infty}
\]
$$
\begin{matrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2 \\
\end{matrix}
$$
\[\begin{matrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2 \\
\end{matrix}
\]
$$
h(\theta) = \sum_{j=0}^n\theta_jx_j
$$
\[h(\theta) = \sum_{j=0}^n\theta_jx_j
\]
$$
\frac{\partial J(\theta)}{\partial\theta_j} = -\frac{1}{m}\sum_{i=0}^m(y^i-h_\theta(x^i))x_j^i
$$
\[\frac{\partial J(\theta)}{\partial\theta_j} = -\frac{1}{m}\sum_{i=0}^m(y^i-h_\theta(x^i))x_j^i
\]
$$
f(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
$$
\[f(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
\]
$$
\left\{
\begin{array}{}
a_1x+b_1y+c_1z = d_1\\
a_2x+b_2y+c_2z = d_2\\
a_3x+b_3y+c_3z = d_3
\end{array}
\right.
$$
\[\left\{
\begin{array}{}
a_1x+b_1y+c_1z = d_1\\
a_2x+b_2y+c_2z = d_2\\
a_3x+b_3y+c_3z = d_3
\end{array}
\right.
\]
$$
X = \left(
\begin{matrix}
x_{11} &x_{12}&\cdots&x_{1d}\\
x_{21} &x_{22}&\cdots&x_{2d}\\
\vdots&\vdots&\ddots&\vdots\\
x_{m1}&x_{m2}&\cdots&x_{md}
\end{matrix}
\right)
= \left(
\begin{matrix}
x_1^T\\
x_2^T\\
\vdots\\
x_m^T\\
\end{matrix}
\right)
$$
\[X = \left(
\begin{matrix}
x_{11} &x_{12}&\cdots&x_{1d}\\
x_{21} &x_{22}&\cdots&x_{2d}\\
\vdots&\vdots&\ddots&\vdots\\
x_{m1}&x_{m2}&\cdots&x_{md}
\end{matrix}
\right)
= \left(
\begin{matrix}
x_1^T\\
x_2^T\\
\vdots\\
x_m^T\\
\end{matrix}
\right)
\]
$$
\begin{align}
\frac{\partial J(\theta)}{\partial \theta_j}
& = -\frac{1}{m}\sum_{i=0}^m(y^i-h_\theta(x^i))\frac{\partial}{\partial\theta_j}(y^i-h_\theta(x^i)) \\
& = -\frac{1}{m}\sum_{i=0}^m(y^i-h_\theta(x^i))\frac{\partial}{\partial\theta_j}(\sum_{j=0}^n\theta_jx_j^i-y^i) \\
& = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x_i^j
\end{align}
$$
\[\begin{align}
\frac{\partial J(\theta)}{\partial \theta_j}
& = -\frac{1}{m}\sum_{i=0}^m(y^i-h_\theta(x^i))\frac{\partial}{\partial\theta_j}(y^i-h_\theta(x^i)) \\
& = -\frac{1}{m}\sum_{i=0}^m(y^i-h_\theta(x^i))\frac{\partial}{\partial\theta_j}(\sum_{j=0}^n\theta_jx_j^i-y^i) \\
& = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x_i^j
\end{align}
\]
$$
\sqrt{x^2+\sqrt{y}} \\
\sqrt[3]{2} \\
$$
\[\sqrt{x^2+\sqrt{y}} \\
\sqrt[3]{2} \\
\]
$$
\overline{m+n} \qquad
\underline{m+n}
$$
\[\overline{m+n} \qquad
\underline{m+n}
\]
$$
\underbrace{a+b+\cdots+z}_{26}
$$
\[\underbrace{a+b+\cdots+z}_{26}
\]
$$
\vec{a} \quad
\overrightarrow{AB}
$$
\[\vec{a} \quad
\overrightarrow{AB}
\]
$$
v = \sigma_1 \cdot \sigma_2 \tau_1 \cdot\tau_2
$$
\[v = \sigma_1 \cdot \sigma_2 \tau_1 \cdot\tau_2
\]
$$
\lim_{x \rightarrow 0} \frac{\sin x}{x}=1
$$
\[\lim_{x \rightarrow 0} \frac{\sin x}{x}=1
\]
$$
\mathop{\min_{G} \max_{D}}
$$
\[\mathop{\min_{G} \max_{D}}
\]
Reference：
