-
$\sqrt[n]{x}$
\sqrt[n]{x} -
$x_i^2, a_{ij}^{kl}, \Gamma_{n}^{k},\sum_{i=1}^{n} x_i,\int_{a}^{b} f(x) \, dx,\lim_{x \to 0} f(x),\textit{f}_a^b$
x_i^2, a_{ij}^{kl}, \Gamma_{n}^{k},\sum_{i=1}^{n} x_i,\int_{a}^{b} f(x) \, dx,\lim_{x \to 0} f(x),\textit{f}_a^b -
$\frac{x}{y} $
\frac{x}{y} - $
\begin{matrix}
a & b & c \newline
d & e & f \newline
g & h & i
\end{matrix}
$
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* 环境名- 语法示例- 效果 * matrix \begin{matrix} ... \end{matrix} abcdabcd (无括号) * pmatrix \begin{pmatrix} ... \end{pmatrix} (abcd)(abcd) (圆括号) * bmatrix \begin{bmatrix} ... \end{bmatrix} [abcd][abcd] (方括号) * Bmatrix \begin{Bmatrix} ... \end{Bmatrix} {abcd}{abcd} (花括号) * vmatrix \begin{vmatrix} ... \end{vmatrix} ∣∣∣abcd∣∣∣ abcd (行列式竖线) * Vmatrix \begin{Vmatrix} ... \end{Vmatrix} ∥∥∥abcd∥∥∥‖abcd‖ (双竖线，范数) \begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} -
$\frac{\partial f}{\partial x},\frac{\partial^2 f}{\partial x \partial y},\frac{\partial (f,g)}{\partial (x,y)} = \begin{vmatrix} \frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} \newline \frac{\partial g}{\partial x} & \frac{\partial g}{\partial y} \end{vmatrix}$
\frac{\partial f}{\partial x},\frac{\partial^2 f}{\partial x \partial y},\frac{\partial (f,g)}{\partial (x,y)} = \begin{vmatrix} \frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} \\ \frac{\partial g}{\partial x} & \frac{\partial g}{\partial y} \end{vmatrix} -
$\nabla$
\nabla - $\alpha$
\alpha -
$\iff$
\iff -
$\implies$
\implies -
$\Delta$
\Delta -
$\mathrm{i}$
\mathrm{i} -
$\approx$
\approx -
$a \leq b ,a \geq b,a\neq b,a \ll b,a \gg b$
a \leq b,a \geq b,a\neq b,a \ll b,a \gg b -
$\mathbf{A + B = C}$
$\mathbf{A + B = C}$ -
集合表示：$A = { x \mid x > 0 }$
集合表示：$A = \{ x \mid x > 0 \}$ - $a \in A$
$a \in A$ - $b \notin A$
$b \notin A$ - $A \subset B$
$A \subset B$ - $A \subsetneq B$
$A \subsetneq B$ - $B \supset A$
$B \supset A$ - $\mathbb{R}$
$\mathbb{R}$ - $p \land q$
$p \land q$ - $p \lor q$
$p \lor q$ -
\[f(x) =
\left\{
\begin{aligned}
& x^2 & \text{if } x > 0 \newline
& 0 & \text{if } x = 0 \newline
& -x^2 & \text{if } x < 0 \newline
\end{aligned}
\right.\]
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$$ f(x) = \left\{ \begin{aligned} & x^2 & \text{if } x > 0 \newline & 0 & \text{if } x = 0 \newline & -x^2 & \text{if } x < 0 \newline \end{aligned} \right. $$
-
$\overline{A}$
$\overline{A}$ -
$A \xrightarrow[\text{下方条件}]{\text{上方条件}} B$
A \xrightarrow[\text{下方条件}]{\text{上方条件}} B -
$\mathbf{a} \times \mathbf{b}$
\mathbf{a} \times \mathbf{b} - \[\min_{\substack{x_1, x_2 }} \left( x_1 + x_2 + P(x_1^2 + x_2^2 - 1) \right)\]
1
2
3
$$
\min_{\substack{x_1, x_2 }} \left( x_1 + x_2 + P(x_1^2 + x_2^2 - 1) \right)
$$
-
$\Downarrow$
\Downarrow -
$\underset{x_1, x_2}{\text{Min.}} \, x_1 + x_2 + \underset{\lambda \geq 0}{\text{Max.}} \, \lambda(x_1^2 + x_2^2 - 1)$
\underset{x_1, x_2}{\text{Min.}} \, x_1 + x_2 + \underset{\lambda \geq 0}{\text{Max.}} \, \lambda(x_1^2 + x_2^2 - 1) - 设矩阵 $A \in \mathbb{R}^{n \times n}$ 为对称矩阵：
- 若 $A \succ 0$，则 $A$ 是严格正定矩阵
- 若 $A \succeq 0$，则 $A$ 是半正定矩阵
- 若 $A \prec 0$，则 $A$ 是严格负定矩阵
- 若 $A \preceq 0$，则 $A$ 是半负定矩阵
- $\forall$
\forall -
$\exists$
\exists -
$\infty$
\infty - $
\frac{\partial L(x,\lambda^,\mu^)}{\partial x}\bigg|{x=x^*} = \nabla f(x^*) + \sum{i=1}^{m} \lambda_i^* \nabla g_i(x^) + \sum_{j=1}^{p} \mu_j^ \nabla h_j(x^*) = 0
$
1 2 3
$ \frac{\partial L(x,\lambda^*,\mu^*)}{\partial x}\bigg|_{x=x^*} = \nabla f(x^*) + \sum_{i=1}^{m} \lambda_i^* \nabla g_i(x^*) + \sum_{j=1}^{p} \mu_j^* \nabla h_j(x^*) = 0 $
- $\gamma$
\gamma - $\eta$
\eta - $\xi$
\xi - $\phi$
\phi - $\psi$
\psi - $\omega$
\omega - $\theta$
\theta - $\lambda$
\lambda - $\lfloor x \rfloor$
\lfloor x \rfloor - $\lceil x \rceil$
\lceil x \rceil
