Mathematician

麦克斯韦方程组 :

$$
\begin{eqnarray}
\nabla\cdot\vec{E} &=& \frac{\rho}{\epsilon_0} \\
\nabla\cdot\vec{B} &=& 0 \\
\nabla\times\vec{E} &=& -\frac{\partial B}{\partial t} \\
\nabla\times\vec{B} &=& \mu_0\left(\vec{J}+\epsilon_0\frac{\partial E}{\partial t} \right)
\end{eqnarray}
$$

块级公式:

$$ x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]

行内公式:

$$ \Gamma(n) = (n-1)!\quad\forall n\in\mathbb N $$

$$ h(x) = \theta_0 + \theta_1 x $$

\begin{equation}\label{eq1}r = r_F+ \beta (r_M - r_F) + \epsilon\end{equation}

行间公式

$$
\theta_i = \theta_i - \alpha\frac\partial{\partial\theta_i}J(\theta)
$$

线性回归算法里的成本函数

$$
J(\theta) = \frac 1 2 \sum_{i=1}^m (h_\theta(x^{(i)})-y^{(i)})^2
$$

希腊字母

alpha A α \alpha beta B β \beta

$$
\begin{array}{c|lcr}
n & \text{Left} & \text{Center} & \text{Right} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i \\
\end{array}
$$

矩阵

$$
\begin{matrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2 \\
\end{matrix}
$$

增广矩阵

$$ \left[
\begin{array}{cc|c}
1&2&3\\
4&5&6
\end{array}
\right]
$$

$$R_{m \times n} = U_{m \times m} S_{m \times n} V_{n \times n}’$$

$$R_{m \times n}$$

$$T(n) = \Theta(n)$$

$$
\Gamma(z) = \int_0^\infty t^{z-1}e^{-t}dt\,.
$$