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机器学习中常用的latex命令

tech2023-01-24  219

参考

妈咪叔

1.希腊字母

希腊字母命令 θ \theta θ\theta μ \mu μ\mu σ \sigma σ\sigma Σ \Sigma Σ\Sigma α \alpha α\alpha β \beta β\beta ξ \xi ξ\xi η \eta η\eta π \pi π\pi λ \lambda λ\lambda Λ \Lambda Λ\Lambda ∞ \infty ∞\infty高斯分布 N \mathcal N N\mathcal N积分 ∫ \int ∫\int

2.关系

关系命令 ∈ \in ∈\in ⊥ \perp ⊥\perp ∃ \exists ∃\exists ∀ \forall ∀\forall ∼ \sim ∼\sim ∣ \mid ∣\mid ≠ \ne ​=\ne ≤ \le ≤\le ≥ \ge ≥\ge ≪ \ll ≪\ll ≫ \gg ≫\gg ∝ \propto ∝\propto × \times ×\times b a \frac{b}{a} ab​\frac{b}{a} ⋅ \cdot ⋅\cdot ⋯ \cdots ⋯\cdots ⋮ \vdots ⋮\vdots ⋱ \ddots ⋱\ddots

3.标

标命令例下标_{} x d o w n x_{down} xdown​x_{down}上标^{} x u p x^{up} xupx^{up} x ^ \hat x x^\hat x a ⃗ \vec{a} a \vec{a} ∼ i.i.d \stackrel{\text{i.i.d}}{\sim } ∼i.i.d\stackrel{\text{i.i.d}}{\sim } ∑ i = 1 N \sum_{i=1}^{N} i=1∑N​\sum_{i=1}^{N} ∏ i = 1 N \prod_{i=1}^{N} i=1∏N​\prod_{i=1}^{N}转置 ⊤ \top ⊤\top A ⊤ A^{\top} A⊤\A^{\top}导数 ′ \prime ′\prime

p ( x ) = 1 2 π σ exp ⁡ { − ( x − μ ) 2 2 σ 2 } p(x)=\frac{1}{\sqrt{2\pi}\sigma}\exp \left \{ -\frac{(x-\mu)^2}{2\sigma^2} \right \} p(x)=2π ​σ1​exp{−2σ2(x−μ)2​} p ( x ) = 1 ( 2 π ) p / 2 ∣ Σ ∣ 1 / 2 exp ⁡ ( − 1 2 ( x − μ ) ⊤ Σ − 1 ( x − μ ) ) p(x)=\frac{1}{(2\pi)^{p/2}\left| \Sigma\right|^{1/2}} \exp( -\frac{1}{2} (x-\mu)^{\top}\Sigma^{-1}(x-\mu)) p(x)=(2π)p/2∣Σ∣1/21​exp(−21​(x−μ)⊤Σ−1(x−μ))

4.对齐/大括号

a a a a = b b = b b b b b \begin{aligned} aaaa &=bb\\ &=bbbbb \end{aligned} aaaa​=bb=bbbbb​

$$\begin{aligned} aaaa &=bb\\ &=bbbbb \end{aligned}$$

在等号处对齐

\begin{aligned} &=\\ &= \end{aligned}

矩阵-左大括号 { a b c 1 2 3 α β η \left \{ \begin{matrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{matrix} \right. ⎩⎨⎧​a1α​b2β​c3η​

$$\left \{ \begin{matrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{matrix} \right.$$

矩阵-右大括号 a b c 1 2 3 α β η } \left . \begin{matrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{matrix} \right \} a1α​b2β​c3η​⎭⎬⎫​

$$\left . \begin{matrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{matrix} \right \}$$

矩阵-双大括号 { a b c 1 2 3 α β η } \begin{Bmatrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{Bmatrix} ⎩⎨⎧​a1α​b2β​c3η​⎭⎬⎫​

$$\begin{Bmatrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{Bmatrix}$$

矩阵-双括号 ( a b c 1 2 3 α β η ) \begin{pmatrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{pmatrix} ⎝⎛​a1α​b2β​c3η​⎠⎞​

$$\begin{pmatrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{pmatrix}$$

矩阵-双中 括号 [ a b c 1 2 3 α β η ] \begin{bmatrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta\\ \end{bmatrix} ⎣⎡​a1α​b2β​c3η​⎦⎤​

$$\begin{bmatrix} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{bmatrix}$$

数组 { a b c 1 2 3 α β η \left \{ \begin{array}{l} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{array} \right . ⎩⎨⎧​a1α​b2β​c3η​

$$\left \{ \begin{array}{l} a & b & c \\ 1 & 2 & 3 \\ \alpha & \beta & \eta \end{array} \right .$$
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