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如何在多个方程式中放置括号

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如何在多个方程式中放置括号

我有以下表达：

\begin{equation}
\begin{aligned}
%C1
\sum_{i = 1}^{m}{y^{C_1}_i} &= m\beta_0^{C_1} + \beta_1^{C_1}\sum_{i = 1}^{m}{x_{i1}^{C_1}} + \cdots + \beta_q^{C_1}\sum_{i = 1}^{m}{x_{iq}^{C_1}}\\
\sum_{i = 1}^{m}{y^{C_1}_ix_{i1}^{C_1}} &= \beta_0^{C_1}\sum_{i = 1}^{m}{x_{i1}^{C_1}} + \beta_1^{C_1}\sum_{i = 1}^{m}{(x_{i1}^{C_1})^2} + \cdots + \beta_q^{C_1}\sum_{i = 1}^{m}{x_{iq}^{C_1}x_{i1}^{C_1}}\\
&\vdots\\
\sum_{i = 1}^{m}{y^{C_1}_ix_{iq}^{C_1}} &= \beta_0^{C_1}\sum_{i = 1}^{m}{x_{iq}^{C_1}} + \beta_1^{C_1}\sum_{i = 1}^{m}{x_{i1}^{C_1}x_{iq}^{C_1}} + \cdots + \beta_q^{C_1}\sum_{i = 1}^{m}{(x_{iq}^{C_1})^2}\\
%C2
\sum_{i = 1}^{m}{y^{C_2}_i} &= m\beta_0^{C_2} + \beta_1^{C_2}\sum_{i = 1}^{m}{x_{i1}^{C_2}} + \cdots + \beta_q^{C_2}\sum_{i = 1}^{m}{x_{iq}^{C_2}}\\
\sum_{i = 1}^{m}{y^{C_2}_ix_{i1}^{C_2}} &= \beta_0^{C_2}\sum_{i = 1}^{m}{x_{i1}^{C_2}} + \beta_1^{C_2}\sum_{i = 1}^{m}{(x_{i1}^{C_2})^2} + \cdots + \beta_q^{C_2}\sum_{i = 1}^{m}{x_{iq}^{C_2}x_{i1}^{C_2}}\\
&\vdots\\
\sum_{i = 1}^{m}{y^{C_2}_ix_{iq}^{C_2}} &= \beta_0^{C_2}\sum_{i = 1}^{m}{x_{iq}^{C_2}} + \beta_1^{C_2}\sum_{i = 1}^{m}{x_{i1}^{C_2}x_{iq}^{C_2}} + \cdots + \beta_q^{C_2}\sum_{i = 1}^{m}{(x_{iq}^{C_2})^2}\\
%R
\sum_{i = 1}^{m}{y^{R}_i} &= m\beta_0^{R} + \beta_1^{R}\sum_{i = 1}^{m}{x_{i1}^{R}} + \cdots + \beta_q^{R}\sum_{i = 1}^{m}{x_{iq}^{R}}\\
\sum_{i = 1}^{m}{y^{R}_ix_{i1}^{R}} &= \beta_0^{R}\sum_{i = 1}^{m}{x_{i1}^{R}} + \beta_1^{R}\sum_{i = 1}^{m}{(x_{i1}^{R})^2} + \cdots + \beta_q^{R}\sum_{i = 1}^{m}{x_{iq}^{R}x_{i1}^{R}}\\
&\vdots\\
\sum_{i = 1}^{m}{y^{R}_ix_{iq}^{R}} &= \beta_0^{R}\sum_{i = 1}^{m}{x_{iq}^{R}} + \beta_1^{R}\sum_{i = 1}^{m}{x_{i1}^{R}x_{iq}^{R}} + \cdots + \beta_q^{R}\sum_{i = 1}^{m}{(x_{iq}^{R})^2}
\end{aligned}
\label{eq:normals_equations}
\end{equation}

我想要放置这种形式的括号：

在此处输入图片描述 太感谢了！

答案1

您可以使用的基本构建块是

\left\{
  \begin{aligned}
     ....
  \end{\aligned}
\right.

如果你想要q+1在前面，那么就把它写在前面\left\{。你想要三个这样的组在不同的行上，显然只有一个方程编号，所以你可以把这些组放在

\begin{equation}
   \begin{gathered}
      ...\\
      ---\\
   \end{gathered}
\end{equation}

给予

示例输出

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\begin{equation}
  \begin{gathered}
    \left\{
      \begin{aligned}
        % C1
        \sum_{i=1}^{m}{y^{C_1}_i}
        &= m\beta_0^{C_1}
        + \beta_1^{C_1}\sum_{i=1}^{m}{x_{i1}^{C_1}} + \dots
        + \beta_q^{C_1}\sum_{i=1}^{m}{x_{iq}^{C_1}}\\
        \sum_{i=1}^{m}{y^{C_1}_ix_{i1}^{C_1}}
        &= \beta_0^{C_1}\sum_{i=1}^{m}{x_{i1}^{C_1}}
        + \beta_1^{C_1}\sum_{i=1}^{m}{(x_{i1}^{C_1})^2} + \dots
        + \beta_q^{C_1}\sum_{i=1}^{m}{x_{iq}^{C_1}x_{i1}^{C_1}}\\
        &\vdots\\
        \sum_{i=1}^{m}{y^{C_1}_ix_{iq}^{C_1}}
        &= \beta_0^{C_1}\sum_{i=1}^{m}{x_{iq}^{C_1}}
        + \beta_1^{C_1}\sum_{i=1}^{m}{x_{i1}^{C_1}x_{iq}^{C_1}}
        + \dots + \beta_q^{C_1}\sum_{i=1}^{m}{(x_{iq}^{C_1})^2}\\
      \end{aligned}
    \right.\\
    % C2
    \left\{
      \begin{aligned}
        \sum_{i=1}^{m}{y^{C_2}_i}
        &= m\beta_0^{C_2}
        + \beta_1^{C_2}\sum_{i=1}^{m}{x_{i1}^{C_2}} + \dots
        + \beta_q^{C_2}\sum_{i=1}^{m}{x_{iq}^{C_2}}\\
        \sum_{i=1}^{m}{y^{C_2}_ix_{i1}^{C_2}}
        &= \beta_0^{C_2}\sum_{i=1}^{m}{x_{i1}^{C_2}}
        + \beta_1^{C_2}\sum_{i=1}^{m}{(x_{i1}^{C_2})^2} + \dots
        + \beta_q^{C_2}\sum_{i=1}^{m}{x_{iq}^{C_2}x_{i1}^{C_2}}\\
        &\vdots\\
        \sum_{i=1}^{m}{y^{C_2}_ix_{iq}^{C_2}}
        &= \beta_0^{C_2}\sum_{i=1}^{m}{x_{iq}^{C_2}}
        + \beta_1^{C_2}\sum_{i=1}^{m}{x_{i1}^{C_2}x_{iq}^{C_2}}
        + \dots + \beta_q^{C_2}\sum_{i=1}^{m}{(x_{iq}^{C_2})^2}\\
      \end{aligned}
    \right.\\
    % R
    \left\{
      \begin{aligned}
        \sum_{i=1}^{m}{y^{R}_i}
        &= m\beta_0^{R} + \beta_1^{R}\sum_{i=1}^{m}{x_{i1}^{R}}
        + \dots + \beta_q^{R}\sum_{i=1}^{m}{x_{iq}^{R}}\\
        \sum_{i=1}^{m}{y^{R}_ix_{i1}^{R}}
        &= \beta_0^{R}\sum_{i=1}^{m}{x_{i1}^{R}}
        + \beta_1^{R}\sum_{i=1}^{m}{(x_{i1}^{R})^2} + \dots
        + \beta_q^{R}\sum_{i=1}^{m}{x_{iq}^{R}x_{i1}^{R}}\\
        &\vdots\\
        \sum_{i=1}^{m}{y^{R}_ix_{iq}^{R}}
        &= \beta_0^{R}\sum_{i=1}^{m}{x_{iq}^{R}}
        + \beta_1^{R}\sum_{i=1}^{m}{x_{i1}^{R}x_{iq}^{R}}
        + \dots + \beta_q^{R}\sum_{i=1}^{m}{(x_{iq}^{R})^2}
      \end{aligned}
    \right.
    \label{eq:normals_equations}
  \end{gathered}
\end{equation}

\end{document}

我已经将您的改为，\cdots因为\dots知道在加号amsmath之间使用哪些点。+

您可以考虑使用\vdotswithin{=}该mathtools包来使垂直点位于等号的中心。

如果要跨组垂直对齐各个元素，请参阅跨“对齐”方程块进行对齐

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