在数学模式下对齐下标

Question

有没有一种简单的方法（也许是通过mathtools对齐正常下标提供的）？

我知道我可以手动完成此操作\vphantom，但我正在寻找更好的方法。

\documentclass{article}

\usepackage{mathtools}

\begin{document}
\noindent Looks pretty bad:
\[
    T_\theta T_\theta^{-1} = \begin{pmatrix*}[r]
        \cos\theta & -\sin\theta\\
        \sin\theta & \cos\theta
    \end{pmatrix*}\begin{pmatrix*}[r]
        \cos\theta & \sin\theta\\
        -\sin\theta & \cos\theta
    \end{pmatrix*}
    = \begin{pmatrix}1&0\\0&1\end{pmatrix} = I
\]
adjustlimits doesn't work:
\[
    \adjustlimits T_\theta T_\theta^{-1} = \begin{pmatrix*}[r]
        \cos\theta & -\sin\theta\\
        \sin\theta & \cos\theta
    \end{pmatrix*}\begin{pmatrix*}[r]
        \cos\theta & \sin\theta\\
        -\sin\theta & \cos\theta
    \end{pmatrix*}
    = \begin{pmatrix}1&0\\0&1\end{pmatrix} = I
\]
vphantom does work
\[
    T_\theta^{\vphantom{-1}} T_\theta^{-1} = \begin{pmatrix*}[r]
        \cos\theta & -\sin\theta\\
        \sin\theta & \cos\theta
    \end{pmatrix*}\begin{pmatrix*}[r]
        \cos\theta & \sin\theta\\
        -\sin\theta & \cos\theta
    \end{pmatrix*}
    = \begin{pmatrix}1&0\\0&1\end{pmatrix} = I
\]
\end{document}

Answer 1

尝试\mathstrut，它恰好是\vphantom(，并且始终将下标放在内{}。

编辑：大师说这个\vphantom{-}概念更好，为了方便，我创建了一个新的命令：

\documentclass{article}
\usepackage{mathtools}
\newcommand{\egreg}{\vphantom{-}}% new command for alignment adjustment (you can choose another name, of course!) 
\begin{document}
    \noindent egreg's version: 
    \[
    T_{\theta}^{\egreg}\, T_{\theta}^{-1} = \begin{pmatrix*}[r] % I've added also a little space \,
    \cos\theta & -\sin\theta\\
    \sin\theta & \cos\theta
    \end{pmatrix*}\begin{pmatrix*}[r]
    \cos\theta & \sin\theta\\
    -\sin\theta & \cos\theta
    \end{pmatrix*}
    = \begin{pmatrix}1&0\\0&1\end{pmatrix} = I
    \]
    \noindent My previous version: 
    \[
    T_{\theta}^{\mathstrut}\, T_{\theta}^{-1} = \begin{pmatrix*}[r] % I've added also a little space \,
    \cos\theta & -\sin\theta\\
    \sin\theta & \cos\theta
    \end{pmatrix*}\begin{pmatrix*}[r]
    \cos\theta & \sin\theta\\
    -\sin\theta & \cos\theta
    \end{pmatrix*}
    = \begin{pmatrix}1&0\\0&1\end{pmatrix} = I
    \]
\end{document}

Answer 2

您可以相应地调整字体尺寸。

\documentclass{article}

\usepackage{mathtools}

\begin{document}
\[
    % Regular subscript positon
    \fontdimen16\textfont2=\dimexpr
        \fontdimen17\textfont2 % subscript position in presence of superscript
      + \fontdimen19\textfont2 % subscript drop in presence of superscript
    \relax
    T_\theta T_\theta^{-1} = \begin{pmatrix*}[r]
        \cos\theta & -\sin\theta\\
        \sin\theta & \cos\theta
    \end{pmatrix*}\begin{pmatrix*}[r]
        \cos\theta & \sin\theta\\
        -\sin\theta & \cos\theta
    \end{pmatrix*}
    = \begin{pmatrix}1&0\\0&1\end{pmatrix} = I
\]
\end{document}

Answer 3

另一个手动解决方法是使用括号将下标与上标分开：

\documentclass{article}
\usepackage{mathtools}

\begin{document}
    \noindent 
    \[
        T_{\theta}\, {T_{\theta}}^{-1} = \begin{pmatrix*}[r] % I've also added also a little space \,
        \cos\theta & -\sin\theta\\
        \sin\theta & \cos\theta
        \end{pmatrix*}\begin{pmatrix*}[r]
        \cos\theta & \sin\theta\\
        -\sin\theta & \cos\theta
        \end{pmatrix*}
        = \begin{pmatrix}1&0\\0&1\end{pmatrix} = I
    \]
\end{document}

最终输出结果中，下标已经对齐，与第一个解法稍有不同：