Math Block for Markdown ［For Typora］

Math Block for Markdown

Code:[Inline Math Formula]

This formula $f(x)=x_{1}^{2}+x_{2}^{2}$is an inline formula

preview:

This formula f(x)=x21+x22 is an inline formula

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Code:[Fraction]

$$
f(x) = x^2+\dfrac{1}{x}
$$

preview:

f(x)=x2+1x

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Code:[Set]

$$
D = \{(x_1,y_1),(x_2,y_2),…,(x_n,y_n)\}
$$

preview:

D={(x1,y1),(x2,y2),…,(xn,yn)}

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Code:[Sum]

$$
　(w^{*},b^{*})= arg  \ min_{\left( w,b\right)} \sum^{n}_{i=1}\left(y_{i}-wx_{i} - b\right)^{2}
$$

preview:

(w∗,b∗)=arg min(w,b)∑i=1n(yi−wxi−b)2

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Code:[Matrix]

$$
X = \begin{bmatrix}
x_{11}&x_{12}&\cdots&x_{1d}&1\\
x_{21}&x_{22}&\cdots&x_{2d}&1\\
\vdots&\vdots&\ddots&\vdots&\vdots\\
x_{n1}&x_{n2}&\cdots&x_{nd}&1\\
\end{bmatrix}
$$

preview:

X=⎡⎣⎢⎢⎢⎢x11x21⋮xn1x12x22⋮xn2⋯⋯⋱⋯x1dx2d⋮xnd11⋮1⎤⎦⎥⎥⎥⎥

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Code:[Piecewise functions]

$$
y = 
\begin{cases}
0, &z<0\cr
0.5, &z=0\cr
1, &z>0\cr
\end{cases}
$$

preview:

y=⎧⎩⎨⎪⎪0,0.5,1,z<0z=0z>0

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Code:[Hat]

$$
Var[\hat{f}(x)] = E[\hat{f}(x)-E[\hat{f}(x)]^2]
$$

preview:

Var[f̂ (x)]=E[f̂ (x)−E[f̂ (x)]2]

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Code:[Set Belonging]

$$
\rho = \dfrac{\sum_{x \in \hat{D}}w_x}{\sum_{x \in D}w_x}
$$

preview:

ρ=∑x∈D̂ wx∑x∈Dwx

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Code:[Arrow]

$$
\lim _{m\rightarrow \infty }\left( 1-\dfrac {1}{m}\right) ^{m}\rightarrow \dfrac{1}{e}
$$

preview:

limm→∞(1−1m)m→1e

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Code:[Integrate]

$$
\int_{0}^{1}x^{2}dx
$$

preview:

∫10x2dx

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Code:[Space]

$$
f(x_i) = wx_i+b  \ \ \ \  s.t.  \  f(x_i) \approx y_i
$$

preview:

f(xi)=wxi+b    s.t. f(xi)≈yi