如何在 LATEX 中格式化矩阵方程组

Question

我目前有以下方程组代码：

\documentclass{article}

\usepackage{amsmath}
\usepackage{etoolbox}

    \newcommand{\dpartial}[2]{\frac{\partial #1}{\partial #2}}

    \AtBeginEnvironment{bmatrix}{\everymath{\displaystyle}} % \displaystyle systems of equations

\begin{document}
 \begin{equation}
    \begin{bmatrix} 
        m\dpartial{u}{T} & m\dpartial{u}{p} \\ 
        -m\left(T\dpartial{R}{T} + R\right) & V - mT\dpartial{R}{p} 
    \end{bmatrix}
    %
    \begin{bmatrix}
        \dot{T} \\ 
        \dot{p} 
    \end{bmatrix} = 
    %
    \begin{bmatrix}
        \dot{Q} - p\dot{V} + \dot{m}(h-u) - m\dpartial{u}{\phi}\dot{\phi}  \\
        \dot{m}RT + mT\dpartial{R}{\phi}\dot{\phi} - p\dot{V} 
    \end{bmatrix}
    \end{equation}
\end{document}

但结果却是这样的：

因此，我的问题是是否有一种方法来格式化方程组，使得包含 T 和 p 的导数的向量可以具有与其相邻矩阵相同的高度。

提前感谢您的帮助。

Answer 1

通过添加\vphantom{\dpartial{u}{p}}到向量元素：

\documentclass{article}

\usepackage{amsmath}
    \newcommand{\dpartial}[2]{\frac{\partial #1}{\partial #2}}
\usepackage{etoolbox}
    \AtBeginEnvironment{bmatrix}{\everymath{\displaystyle}} % \displaystyle systems of equations

\begin{document}
 \begin{equation}
    \begin{bmatrix}
        m\dpartial{u}{T} & m\dpartial{u}{p} \\
        -m\left(T\dpartial{R}{T} + R\right) & V - mT\dpartial{R}{p}
    \end{bmatrix}
    %
    \begin{bmatrix}
        \dot{T}\vphantom{\dpartial{u}{p}} \\
        \dot{p}\vphantom{\dpartial{u}{p}}
    \end{bmatrix} =
    %
    \begin{bmatrix}
        \dot{Q} - p\dot{V} + \dot{m}(h-u) - m\dpartial{u}{\phi}\dot{\phi}  \\
        \dot{m}RT + mT\dpartial{R}{\phi}\dot{\phi} - p\dot{V}
    \end{bmatrix}
    \end{equation}
\end{document}

附录： 考虑到@Mico 的评论，通过在行之间插入一些垂直空间，您将获得更好看的矩阵和向量。您可以通过多种方式实现这一点，例如：

• 通过终止行\\[2ex]
• 通过\addlinespace在包中插入确定booktabs：

\documentclass{article}
\usepackage{booktabs}

\usepackage{amsmath}
    \newcommand{\dpartial}[2]{\frac{\partial #1}{\partial #2}}
\usepackage{etoolbox}
    \AtBeginEnvironment{bmatrix}{\everymath{\displaystyle}} % \displaystyle systems of equations

\begin{document}
 \begin{equation}
    \begin{bmatrix}
        m\dpartial{u}{T} & m\dpartial{u}{p} \\
        \addlinespace
        -m\biggl(T\dpartial{R}{T} + R\biggr) & V - mT\dpartial{R}{p}
    \end{bmatrix}
    %
    \begin{bmatrix}
        \dot{T}\vphantom{\dpartial{u}{p}} \\
        \addlinespace
        \dot{p}\vphantom{\dpartial{u}{p}}
    \end{bmatrix} =
    %
    \begin{bmatrix}
        \dot{Q} - p\dot{V} + \dot{m}(h-u) - m\dpartial{u}{\phi}\dot{\phi}  \\
        \addlinespace
        \dot{m}RT + mT\dpartial{R}{\phi}\dot{\phi} - p\dot{V}
    \end{bmatrix}
    \end{equation}
\end{document}

• 通过使用包\makegapedcells中定义makecell：

\documentclass{article}
\usepackage{makecell}

\usepackage{amsmath}
    \newcommand{\dpartial}[2]{\frac{\partial #1}{\partial #2}}
\usepackage{etoolbox}
    \AtBeginEnvironment{bmatrix}{\everymath{\displaystyle}} % \displaystyle systems of equations

\begin{document}
 \begin{equation}
\setcellgapes{5pt}
\makegapedcells
    \begin{bmatrix}
        m\dpartial{u}{T} & m\dpartial{u}{p} \\
        -m\biggl(T\dpartial{R}{T} + R\biggr) & V - mT\dpartial{R}{p}
    \end{bmatrix}
    %
    \begin{bmatrix}
        \dot{T}\vphantom{\dpartial{u}{p}} \\
        \dot{p}\vphantom{\dpartial{u}{p}}
    \end{bmatrix} =
    %
    \begin{bmatrix}
        \dot{Q} - p\dot{V} + \dot{m}(h-u) - m\dpartial{u}{\phi}\dot{\phi}  \\
        \dot{m}RT + mT\dpartial{R}{\phi}\dot{\phi} - p\dot{V}
    \end{bmatrix}
    \end{equation}
\end{document}

Answer 2

使用{NiceArray}，nicematrix您可以在数组的前导中添加分隔符。您不需要\vphantom。

\documentclass{article}
\usepackage{nicematrix}
\newcommand{\dpartial}[2]{\frac{\partial #1}{\partial #2}}

\begin{document}
\begin{equation*}
\everymath{\displaystyle}
\begin{NiceArray}{[cc][c]}
m\dpartial{u}{T} & m\dpartial{u}{p} & \dot{T} \\  
-m\left(T\dpartial{R}{T} + R\right) & V - mT\dpartial{R}{p} & \dot{p} 
\end{NiceArray}
=
\begin{bmatrix}
\dot{Q} - p\dot{V} + \dot{m}(h-u) - m\dpartial{u}{\phi}\dot{\phi}  \\
\dot{m}RT + mT\dpartial{R}{\phi}\dot{\phi} - p\dot{V} 
\end{bmatrix}
\end{equation*}
\end{document}

您需要多次编译（因为nicematrix使用 PGF/Tikz 节点）。