Markdown数学公式_累加 markdomn

运算

四则运算

高级运算

对数指数

三角函数

微积分

线性代数

（1）不带括号
0 1 3 3 2 5 7 8 6

$$\begin{matrix} 0 & 1 & 3 \\ 3 & 2 & 5 \\ 7 & 8 & 6 \end{matrix}$$ 037​128​356​

$$\begin{matrix}  0 & 1 & 3 \\  3 & 2 & 5 \\ 7 & 8 & 6  \end{matrix}$$
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（2）带括号
\qquad \qquad \qquad \qquad ( 1 2 3 4 1 3 4 1 1 4 1 2 1 1 2 3 ) \left(

$$\begin{matrix} 1 & 2 & 3 & 4 \\ 1 & 3 & 4 & 1 \\ 1 & 4 & 1 & 2 \\ 1 & 1 & 2 & 3 \end{matrix}$$ \right) ⎝⎜⎜⎛​1111​2341​3412​4123​⎠⎟⎟⎞​ $\left[\begin{array}{c}11\\ 14\\ 21\\ 4\end{array}\right]$ $\left\{\begin{array}{ccccc}a& b& c& d& e\\ f& g& h& i& j\\ k& l& m& n& o\\ p& q& r& s& t\end{array}\right\}$

$\left( \begin{matrix} 1 & 2 & 3 & 4 \\ 1 & 3 & 4 & 1 \\ 1 & 4 & 1 & 2 \\ 1 & 1 & 2 & 3 \end{matrix} \right)$
$\left[ \begin{matrix}  11 \\  14 \\  21 \\  4 \end{matrix} \right]$    
$\left\{ \begin{matrix} a & b & c & d & e\\ f & g & h & i & j \\ k & l & m & n & o \\ p & q & r & s & t \end{matrix} \right\}$
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（3）前面加个参数
A = ( 1 2 3 4 1 3 4 1 1 4 1 2 1 1 2 3 ) (1) A=\left(

$$\begin{matrix} 1 & 2 & 3 & 4 \\ 1 & 3 & 4 & 1 \\ 1 & 4 & 1 & 2 \\ 1 & 1 & 2 & 3 \end{matrix}$$ \right) \tag{1} A=⎝⎜⎜⎛​1111​2341​3412​4123​⎠⎟⎟⎞​(1)

$$A=\left( \begin{matrix} 1 & 2 & 3 & 4 \\ 1 & 3 & 4 & 1 \\ 1 & 4 & 1 & 2 \\ 1 & 1 & 2 & 3 \end{matrix} \right) \tag{1}$$
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（4）行列式
A = ∣ 1 2 3 4 1 3 4 1 1 4 1 2 1 1 2 3 ∣ (2) A=\left|

$$\begin{matrix} 1 & 2 & 3 & 4 \\ 1 & 3 & 4 & 1 \\ 1 & 4 & 1 & 2 \\ 1 & 1 & 2 & 3 \end{matrix}$$ \right| \tag{2} A=∣∣∣∣∣∣∣∣​1111​2341​3412​4123​∣∣∣∣∣∣∣∣​(2)

$$A=\left| \begin{matrix} 1 & 2 & 3 & 4 \\ 1 & 3 & 4 & 1 \\ 1 & 4 & 1 & 2 \\ 1 & 1 & 2 & 3 \end{matrix} \right| \tag{2}$$
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（5）矩阵中间有省略号
水平方向的省略号：\cdots。竖直方向的省略号：\vdots。斜线方向的省略号：\ddots
A = { a b ⋯ e f g ⋯ j ⋮ ⋮ ⋱ ⋮ p q ⋯ t } A= \left\{

$$\begin{matrix} a & b & \cdots & e\\ f & g & \cdots & j \\ \vdots & \vdots & \ddots & \vdots \\ p & q & \cdots & t \end{matrix}$$ \right\} A=⎩⎪⎪⎪⎨⎪⎪⎪⎧​af⋮p​bg⋮q​⋯⋯⋱⋯​ej⋮t​⎭⎪⎪⎪⎬⎪⎪⎪⎫​

$$A= \left\{ \begin{matrix} a & b & \cdots & e\\ f & g & \cdots & j \\ \vdots & \vdots & \ddots & \vdots \\ p & q & \cdots & t \end{matrix} \right\}$$
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逻辑运算

集合运算

表达式

递等式

a = 1 π ∫ − π π f ( x ) cos ⁡ n x   d x = ! = 1 π ∫ − π π x 2 sin ⁡ n x   d x

$$\begin{aligned} a&=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x) \cos nx\,\mathrm{d}x=\\ &!=\frac{1}{\pi}\int_{-\pi}^{\pi}x^2 \sin nx\,\mathrm{d}x \\[6pt] \end{aligned}$$ a​=π1​−π∫π​f(x)cosnxdx=!=π1​∫−ππ​x2sinnxdx​

G = 3 5 E n t ( D 1 ) + 2 5 E n t ( D 2 ) = 3 5 ( − 2 3 log ⁡ 2 2 3 − 1 3 log ⁡ 2 1 3 ) + 2 5 ( − 2 2 log ⁡ 2 2 2 ) = 0.97 − 0.55 = 0.42

$$\begin{aligned} G&=\frac{3}{5}Ent(D_1)+\frac{2}{5}Ent(D_2) \\ & = \frac{3}{5} (-\frac{2}{3}\log_{2}\frac{2}{3} - \frac{1}{3}\log_{2}\frac{1}{3} ) + \frac{2}{5} ( -\frac{2}{2}\log_{2}\frac{2}{2}) \\ & = 0.97-0.55 \\ & = 0.42 \\ \end{aligned}$$ G​=53​Ent(D1​)+52​Ent(D2​)=53​(−32​log2​32​−31​log2​31​)+52​(−22​log2​22​)=0.97−0.55=0.42​

$$\begin{aligned}
a&=\frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x) \cos nx\,\mathrm{d}x=\\
&!=\frac{1}{\pi}\int_{-\pi}^{\pi}x^2 \sin nx\,\mathrm{d}x
\\[6pt]
\end{aligned}
$$
$\begin{aligned}
G&=\frac{3}{5}Ent(D_1)+\frac{2}{5}Ent(D_2) \\
& =  \frac{3}{5} (-\frac{2}{3}\log_{2}\frac{2}{3} - \frac{1}{3}\log_{2}\frac{1}{3} ) + \frac{2}{5} ( -\frac{2}{2}\log_{2}\frac{2}{2}) 	\\
& = 0.97-0.55                          \\
& = 0.42      							\\
\end{aligned}$
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推导式

B = − ∂ × E E = ∂ × B − 4 π j B = − ∂ × E } ⟶ 箭 头 没 法 加 长 了 Maxwell’s equations

$$\begin{aligned} \left.\begin{aligned} B &=-\partial \times E\\ E &=\partial \times B - 4\pi j \\ B &=-\partial \times E\\ \end{aligned}$$ \right \} \stackrel{箭头没法加长了}{\longrightarrow} \qquad \text{Maxwell's equations} \end{aligned} BEB​=−∂×E=∂×B−4πj=−∂×E​⎭⎪⎬⎪⎫​⟶箭头没法加长了​Maxwell’s equations​

1 = x + y 2 = x y 3 = ∂ x + y ∂ x 4 = ∂ x y ∂ x

$$\begin{aligned} 1 &= x + y & \quad 2 &= \frac{x}{y} \\ 3 &= \frac{\partial x + y}{\partial x} & 4 &= \frac{\partial \frac{x}{y}}{\partial x} \end{aligned}$$ 13​=x+y=∂x∂x+y​​24​=yx​=∂x∂yx​​​

$$
\begin{aligned}
 \left.\begin{aligned}
        B &=-\partial \times E\\    
        E &=\partial \times B - 4\pi j \\
         B &=-\partial \times E\\    
       \end{aligned}
 \right \}		\stackrel{箭头没法加长了}{\longrightarrow} 				
 \qquad \text{Maxwell's equations}
\end{aligned}
$$
$$\begin{aligned}
1 &= x + y  & \quad 2 &= \frac{x}{y} \\	
3 &= \frac{\partial x + y}{\partial x} & 4 &= \frac{\partial \frac{x}{y}}{\partial x}
\end{aligned}$$
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text文字表达

$$z=\stackrel{\text{complex number}}{\overbrace{\underset{\text{real}}{\underbrace{x}}+i+\underset{\text{imaginary}}{\underbrace{y}}}}$$

$$
z = \overbrace{
   \underbrace{x}_\text{real} + i + \underbrace{y}_\text{imaginary}
  }^\text{complex number}
$$
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分段函数

u ( x ) = { x 2 if  x ≥ 0 2 x if  x < 0 u(x) =

$$\begin{cases} x^2 & \text{if } x \geq 0 \\ 2x & \text{if } x < 0 \end{cases}$$ u(x)={x22x​if x≥0if x<0​

$$
u(x) = 
  \begin{cases} 
   x^2     & \text{if } x \geq 0 \\
   2x       & \text{if } x < 0
  \end{cases}
$$
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方程组

{ a 1 x + b 1 y + c 1 z = d 1 a 2 x + b 2 y + c 2 z = d 2 a 3 x + b 3 y + c 3 z = d 3 \left\{

$$\begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array}$$ \right. ⎩⎨⎧​a1​x+b1​y+c1​z=d1​a2​x+b2​y+c2​z=d2​a3​x+b3​y+c3​z=d3​​

$$
\left\{ 
\begin{array}{c}
    a_1x+b_1y+c_1z=d_1 \\ 
    a_2x+b_2y+c_2z=d_2 \\ 
    a_3x+b_3y+c_3z=d_3
\end{array}
\right. 
$$
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带方框的等式

x 2 + y 2 = z 2

$$\begin{aligned} \boxed{x^2+y^2 = z^2} \end{aligned}$$ x2+y2=z2​​

$$
\begin{aligned}
 \boxed{x^2+y^2 = z^2}
\end{aligned}
$$
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符号

希腊字母

普通英文字母与加美元符的对比
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$
a b c d e f g h i j k l m n o p q r s t u v w x y z
$abcdefghijklmnopqrstuvwxyz$

数学符号

导数

积分

微分

逻辑

箭头

括号

定界符与组合

上标、下标与组合

汉字、字体与格式

占符号

标点符号

其他

参考资料：
typora-数学符号：https://blog.csdn.net/wait_for_eva/article/details/84307306