使用總結——在markdown中用Latex編寫複雜數學公式

一、多行公式對齊

1.1在等號處對齊

$\left\{ \begin{aligned} \eta_{1} &=a+b x_{1}+\varepsilon_{1} \\ \eta_{2} &=a+b x_{2}+\varepsilon_{2} \\ & \dots \ldots \ldots \\ \eta_{n} &=a+b x_{n}+\varepsilon_{n} \\ \varepsilon_{1} &,\varepsilon_{2}…\varepsilon_{n} \overset{iid} \sim N\left(0, \sigma^{2}\right) \end{aligned} \right.$
多行公式等號對齊的話，最後一行的表示：$\varepsilon_{1} ,\varepsilon_{2}…\varepsilon_{n} \overset{iid} \sim N\left(0, \sigma^{2}\right)$沒有等號，需要好好利用符號&進行調整，使整個括號內的多行公式仍然達到左對齊的效果。
對應語法：

$$\left\{
\begin{aligned} 
\eta_{1} &=a+b x_{1}+\varepsilon_{1} \\
\eta_{2} &=a+b x_{2}+\varepsilon_{2} \\
& \dots \ldots \ldots \\
\eta_{n} &=a+b x_{n}+\varepsilon_{n} \\
\varepsilon_{1} &,\varepsilon_{2}…\varepsilon_{n}  
 \overset{iid} \sim N\left(0, \sigma^{2}\right)
\end{aligned}
\right.
$$

1.2 多行公式左對齊

$\left\{\begin{array}{l} {\eta_{1} =a+b x_{1}+\varepsilon_{1} }\\ {\eta_{2} =a+b x_{2}+\varepsilon_{2}}\\ \dots \ldots \ldots \\ {\eta_{m} =a+b x_{m}+\varepsilon_{m}}\\ {\varepsilon_{1} ,\varepsilon_{2}…\varepsilon_{m} \overset{iid} \sim N\left(0, \sigma^{2}\right)}\\ {\eta_{i} \sim N\left(b_{0}+b_{1} x_{i1}+b_{2} x_{i2}+\cdots+b_{m} x_{im}, \sigma^{2}\right)\quad(i=1,2, \cdots, m)} \end{array}\right.$
可以看到多行公式左對齊時，公式之間的行間距會略微縮小。
對應語法：

$$
\left\{\begin{array}{l}
{\eta_{1} =a+b x_{1}+\varepsilon_{1} }\\
{\eta_{2} =a+b x_{2}+\varepsilon_{2}}\\
\dots \ldots \ldots \\
{\eta_{m} =a+b x_{2}+\varepsilon_{m}}\\
{\varepsilon_{1} ,\varepsilon_{2}…\varepsilon_{m}   
\overset{iid} \sim N\left(0, \sigma^{2}\right)}\\
{\eta_{i} \sim N\left(b_{0}+b_{1} x_{i1}+b_{2} x_{i2}+\cdots+b_{m} x_{im}, \sigma^{2}\right)\quad(i=1,2, \cdots, m)}
\end{array}\right.
$$

1.3 多行公式標整體序號，居中

1.4 多行公式標單行序號

二、矩陣

1.1 示例1

$L= \left[ \begin {array}{cccc} {l_{11}} &{l_{12}} & {\cdots} & {l_{1 m}} \\ {l_{21}} &{l_{22}} & {\cdots} & {l_{2 m}} \\ {\vdots} & {\vdots} & {\cdots} & {\vdots} \\ {l_{m1}} &{l_{m2}} & {\cdots} & {l_{m m}} \\ \end {array} \right]=\left(l_{ij}\right)$
對應語法爲：

$$
L=
\left[ 
\begin
{array}{cccc}
 {l_{11}} &{l_{12}} & {\cdots} & {l_{1 m}} \\ 
 {l_{21}} &{l_{22}} & {\cdots} & {l_{2 m}} \\ 
 {\vdots} & {\vdots} & {\cdots} & {\vdots} \\ 
 {l_{m1}} &{l_{m2}} & {\cdots} & {l_{m m}} \\ 
\end
{array}
\right]=\left(l_{ij}\right)
$$

1.2 示例2

$\left( \begin {array}{cccc} {l_{11}} & {l_{12}} & {\cdots} & {l_{1 m}} \\ {l_{21}} & {l_{22}} & {\cdots} & {l_{2 m}} \\ {\vdots} & {\vdots} & { } & {\vdots} \\ {l_{m 1}} & {l_{m 2}} & {\cdots} & {l_{m m}}\end{array}\right) \left( \begin{array}{c}{\hat{b}_{1}} \\ {\hat{b}_{2}} \\ {\vdots} \\ {\hat{b}_{m}}\end{array}\right)=\left( \begin{array}{c}{l_{1 y}}\\ {l_{2 y}} \\ {\vdots} \\ {l_{m y}}\end{array}\right)$
對應語法：

$$
\left(
 \begin
 {array}{cccc}
 {l_{11}} & {l_{12}} & {\cdots} & {l_{1 m}} \\ 
 {l_{21}} & {l_{22}} & {\cdots} & {l_{2 m}} \\
  {\vdots} & {\vdots} & { } & {\vdots} \\ 
  {l_{m 1}} & {l_{m 2}} & {\cdots} &{l_{mm}}\end{array}\right) \left( \begin{array}{c}{\hat{b}_{1}} \\ 
  {\hat{b}_{2}} \\ 
  {\vdots} \\ 
  {\hat{b}_{m}}\end{array}\right)=\left( \begin{array}{c}{l_{1 y}}\\ 
  {l_{2 y}} \\ 
   {\vdots} \\ {l_{m y}}\end{array}\right)
$$ 

Reference:

1. Latex 箭頭、下標、符號上下寫文字、正方形和三角形 - Zhang’s Wikipedia - CSDN博客