MathJax 数学公式

MathJax 向量

$$
\overrightarrow{v} = \left( \begin{array}{c} 1 \\\\ 2 \end{array} \right)
$$

\[\overrightarrow{v} = \left( \begin{array}{c} 1 \\\\ 2 \end{array} \right)\]

方括号矩阵

$$
A =
\begin{bmatrix}
  1 & 0 & 2 \\\\
  -2 & 1 & 3
\end{bmatrix}
$$

\[A = \begin{bmatrix} 1 & 0 & 2 \\\\ -2 & 1 & 3 \end{bmatrix}\]

矩阵运算

$$
\begin{bmatrix}
  x_{a} \\\\
  y_{a} \\\\
  1
\end{bmatrix}
=
\begin{bmatrix}
  cos(\theta) & -sin(\theta) & \delta_{x} \\\\
  sin(\theta) & cos(\theta) & \delta_{y} \\\\
  0 & 0 & 1
\end{bmatrix}
\begin{bmatrix}
  x_{b} \\\\
  y_{b} \\\\
  1
\end{bmatrix}
$$

\[\begin{bmatrix} x_{a} \\\\ y_{a} \\\\ 1 \end{bmatrix} = \begin{bmatrix} cos(\theta) & -sin(\theta) & \delta_{x} \\\\ sin(\theta) & cos(\theta) & \delta_{y} \\\\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x_{b} \\\\ y_{b} \\\\ 1 \end{bmatrix}\]

方括号竖线矩阵

绘制竖实线，如{cc

cc}

$$
\left[
  \begin{array}{cc|cc}
    1 & 2 & 1 & 0 \\\\
    4 & 5 & 0 & 1
  \end{array}
\right]
$$

\[\left[ \begin{array}{cc|cc} 1 & 2 & 1 & 0 \\\\ 4 & 5 & 0 & 1 \end{array} \right]\]

绘制竖虚线，如{cc:cc}

$$
\left[
  \begin{array}{cc:cc}
    1 & 2 & 1 & 0 \\\\
    4 & 5 & 0 & 1
  \end{array}
\right]
$$

\[\left[ \begin{array}{cc:cc} 1 & 2 & 1 & 0 \\\\ 4 & 5 & 0 & 1 \end{array} \right]\]

MathJax 多行公式对齐

$$
\begin{equation}
\begin{split}
\hat x_{n,n} &= w_1 \cdot z_n + (1-w_1) \cdot \hat x_{n,n-1} \\\\ 
&= w_1 \cdot z_n + \hat x_{n,n-1} - w_1 \cdot \hat x_{n,n-1} \\\\
&= \hat x_{n,n-1} + w_1 \cdot (z_n - \hat x_{n,n-1})
\end{split}
\nonumber
\end{equation}
$$

\[\begin{equation} \begin{split} \hat x_{n,n} &= w_1 \cdot z_n + (1-w_1) \cdot \hat x_{n,n-1} \\\\ &= w_1 \cdot z_n + \hat x_{n,n-1} - w_1 \cdot \hat x_{n,n-1} \\\\ &= \hat x_{n,n-1} + w_1 \cdot (z_n - \hat x_{n,n-1}) \end{split} \nonumber \end{equation}\]

MathJax 方程组

$$
\begin{cases}
  \ x + 2y + 3z = 6 \\\\
  2x - 3y + 2z = 14 \\\\
  3x + \ y - \ z = -2
\end{cases}
$$

\[\begin{cases} \ x + 2y + 3z = 6 \\\\ 2x - 3y + 2z = 14 \\\\ 3x + \ y - \ z =-2 \end{cases}\]