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将矩阵置于箭头之上

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将矩阵置于箭头之上

我想重新使用论文中使用的符号，但在 LaTeX 中格式化它时遇到了麻烦。我试图将一个小的（2x2 或 2x1 矩阵）放在箭头的顶部或右侧。我想要类似这样的内容（但矩阵用圆括号代替方括号）： enter image description here

我已尝试排版底行，这是我的尝试和输出：

\begin{displaymath}
    \xymatrix{ G_{1} \oplus F_{2} \ar[r]^{\begin{psmallmatrix}- $\psi_{1}$ & 0 \\ g & \phi_2 \end{psmallmatrix}} 
 & F_{1} \oplus G_{2} \ar[r]^{\begin{psmallmatrix}- $\phi_{1}$ & 0 \\f & $\psi_2$ \end{psmallmatrix}} } 
& $G_{1} \oplus F_{2}$ }
\end{displaymath}

....... attempt

我正在使用 xy 和 mathtools 包。

答案1

需要增加行距和列距。第一种实现对我更有吸引力，第二种实现与原图类似。

该语句@R+1pc将行距增加1pc = 12pt；同样@C+1pc。

\documentclass{article}
\usepackage{amsmath}
\usepackage[all,cmtip]{xy}

\newcommand{\spmat}[1]{%
  \left(\begin{smallmatrix}#1\end{smallmatrix}\right)%
}

\begin{document}

\begin{equation*}
\xymatrix@C+2pc{
  G_{1} \oplus F_{2} \ar[r]^{\spmat{-\psi_{1} & 0 \\ g & \phi_2}}
  &
  F_{1} \oplus G_{2} \ar[r]^{\spmat{-\phi_{1} & 0 \\f & \psi_2}}
  &
  G_{1} \oplus F_{2}
}
\end{equation*}

\begin{equation*}
\xymatrix@R+1pc@C+2pc{
  F_2 \ar[r]^{\phi_2} \ar[d]^{\spmat{0 \\ 1_{F_2}}}
  &
  G_2 \ar[r]^{\psi_2} \ar[d]^{\spmat{0 \\ 1_{G_2}}}
  &
  F_2 \ar[d]^{\spmat{0 \\ 1_{F_2}}}
  \\
  G_1\oplus F_1 \ar[r]^{\spmat{-\psi_1 & 0 \\ g & \psi_2}}
  &
  F_1\oplus G_2 \ar[r]^{\spmat{-\phi_1 & 0 \\ f & \psi_2}}
  &
  G_1\oplus F_2
}
\end{equation*}

\begin{equation*}
\xymatrix@C+3pc{
  F_2 \ar[r]^{\phi_2} \ar[d]^{\spmat{0 \\ 1_{F_2}}}
  &
  G_2 \ar[r]^{\psi_2} \ar[d]^{\spmat{0 \\ 1_{G_2}}}
  &
  F_2 \ar[d]^{\spmat{0 \\ 1_{F_2}}}
  \\
  G_1\oplus F_1 \ar[r]^{\spmat{-\psi_1 & 0 \\ g & \psi_2}}
  &
  F_1\oplus G_2 \ar[r]^{\spmat{-\phi_1 & 0 \\ f & \psi_2}}
  &
  G_1\oplus F_2
}
\end{equation*}

\end{document}

enter image description here

在嵌套数组时需要tikz-cd小心tikzcd。

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}

\begingroup\lccode`~=`& \lowercase{\endgroup
\newcommand{\spmat}[1]{%
  \left(
  \let~=&
  \begin{smallmatrix}#1\end{smallmatrix}
  \right)
}}

\begin{document}

\begin{equation*}
\begin{tikzcd}
  G_{1} \oplus F_{2} \arrow[r,"\spmat{-\psi_{1} & 0 \\ g & \phi_2}"]
  &
  F_{1} \oplus G_{2} \arrow[r,"\spmat{-\phi_{1} & 0 \\f & \psi_2}"]
  &
  G_{1} \oplus F_{2}
\end{tikzcd}
\end{equation*}


\begin{equation*}
\begin{tikzcd}[column sep=huge,row sep=large]
  F_2 \arrow[r,"\phi_2"] \arrow[d,"\spmat{0 \\ 1_{F_2}}"]
  &
  G_2 \arrow[r,"\psi_2"] \arrow[d,"\spmat{0 \\ 1_{G_2}}"]
  &
  F_2 \arrow[d,"\spmat{0 \\ 1_{F_2}}"]
  \\
  G_1\oplus F_1 \arrow[r,"\spmat{-\psi_1 & 0 \\ g & \psi_2}"]
  &
  F_1\oplus G_2 \arrow[r,"\spmat{-\phi_1 & 0 \\ f & \psi_2}"]
  &
  G_1\oplus F_2
\end{tikzcd}
\end{equation*}

\begin{equation*}
\begin{tikzcd}[column sep=4pc]
  F_2 \arrow[r,"\phi_2"] \arrow[d,"\spmat{0 \\ 1_{F_2}}"]
  &
  G_2 \arrow[r,"\psi_2"] \arrow[d,"\spmat{0 \\ 1_{G_2}}"]
  &
  F_2 \arrow[d,"\spmat{0 \\ 1_{F_2}}"]
  \\
  G_1\oplus F_1 \arrow[r,"\spmat{-\psi_1 & 0 \\ g & \psi_2}"]
  &
  F_1\oplus G_2 \arrow[r,"\spmat{-\phi_1 & 0 \\ f & \psi_2}"]
  &
  G_1\oplus F_2
\end{tikzcd}
\end{equation*}

\end{document}

enter image description here

可以避免上述尴尬（但安全）的技巧，仍然\spmat像 Xy-pic 案例中那样定义。缺点是需要tikzcd以略有不同的方式输入（仅在需要嵌套数组时）：

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}

\newcommand{\spmat}[1]{%
  \left(
  \begin{smallmatrix}#1\end{smallmatrix}
  \right)
}

\begin{document}

\begin{equation*}
\begin{tikzcd}[ampersand replacement=\&,column sep=huge]
  G_{1} \oplus F_{2} \arrow[r,"\spmat{-\psi_{1} & 0 \\ g & \phi_2}"]
  \&
  F_{1} \oplus G_{2} \arrow[r,"\spmat{-\phi_{1} & 0 \\f & \psi_2}"]
  \&
  G_{1} \oplus F_{2}
\end{tikzcd}
\end{equation*}

\begin{equation*}
\begin{tikzcd}[ampersand replacement=\&,column sep=huge,row sep=large]
  F_2 \arrow[r,"\phi_2"] \arrow[d,"\spmat{0 \\ 1_{F_2}}"]
  \&
  G_2 \arrow[r,"\psi_2"] \arrow[d,"\spmat{0 \\ 1_{G_2}}"]
  \&
  F_2 \arrow[d,"\spmat{0 \\ 1_{F_2}}"]
  \\
  G_1\oplus F_1 \arrow[r,"\spmat{-\psi_1 & 0 \\ g & \psi_2}"]
  \&
  F_1\oplus G_2 \arrow[r,"\spmat{-\phi_1 & 0 \\ f & \psi_2}"]
  \&
  G_1\oplus F_2
\end{tikzcd}
\end{equation*}

\begin{equation*}
\begin{tikzcd}[ampersand replacement=\&,column sep=4pc]
  F_2 \arrow[r,"\phi_2"] \arrow[d,"\spmat{0 \\ 1_{F_2}}"]
  \&
  G_2 \arrow[r,"\psi_2"] \arrow[d,"\spmat{0 \\ 1_{G_2}}"]
  \&
  F_2 \arrow[d,"\spmat{0 \\ 1_{F_2}}"]
  \\
  G_1\oplus F_1 \arrow[r,"\spmat{-\psi_1 & 0 \\ g & \psi_2}"]
  \&
  F_1\oplus G_2 \arrow[r,"\spmat{-\phi_1 & 0 \\ f & \psi_2}"]
  \&
  G_1\oplus F_2
\end{tikzcd}
\end{equation*}

\end{document}

答案2

一个具有 的解tikz-cd和一个具有 的解pstricks：

\documentclass{article}
\usepackage{mathtools}
\usepackage{tikz-cd}
\newcommand{\mymatrix}[1]{\begin{psmallmatrix} #1 \end{psmallmatrix}}
\usepackage{pst-node} 
\usepackage{auto-pst-pdf} %% to compile pstricks code with pdflatex

\begin{document}

 \[  \begin{tikzcd}[arrows=-stealth, ampersand replacement=\&, column sep=4em, row sep=3em]%[column sep=-0.5em, row sep=0.8em]
F_2 \dar{\mymatrix{0\\\mkern-5mu\mathbf{1}_{F_2\mkern-4mu}}}\rar{\phi_2} \& G_2 \dar{\mymatrix{0\\\mkern-5mu\mathbf{1}_{G_2\mkern-4mu}}}\rar{\psi_2} \& F_2\dar{\mymatrix{0\\\mkern-5mu\mathbf{1}_{F_2\mkern-4mu}}}\\
G_1\oplus F_2\rar{\mymatrix{\mkern-5mu-\psi_1\! & 0\\g &\phi_2\mkern-4mu}} \& F_1\oplus G_2 \rar{\mymatrix{\mkern-5mu-\phi_1\! & 0\\ f &\psi_2\mkern-4mu}} \& G_1\oplus F_2
\end{tikzcd} \]
\bigskip

\[ \begin{psmatrix}[rowsep=1.25cm, colsep=1.6cm]
%% Nodes
  F_2 & G_2 & F_2 \\
G_1\oplus F_2 & F_1\oplus G_2 & G_1\oplus F_2
%% Arrows and labels%
\everypsbox{\scriptstyle}
\psset{linewidth=0.6pt, arrows=->, arrowinset=0.15, nodesep=2pt, labelsep=3pt}
%% Horizontal arrows
\ncline{1,1}{1,2}\naput{\phi_2}
\ncline{1,2}{1,3}\naput{\psi_2}
\ncline{2,1}{2,2}\naput{\mymatrix{\mkern-5mu-\psi_1\! & 0\\g &\phi_2\mkern-4mu}}
\ncline{2,2}{2,3}\naput{\mymatrix{\mkern-5mu-\phi_1\! & 0\\ f &\psi_2\mkern-4mu}}
%% Vertical arrows
\psset{npos=0.45}
\ncline{1,1}{2,1}\naput{\mymatrix{0\\\mkern-5mu\mathbf{1}_{F_2\mkern-4mu}}}
\ncline{1,2}{2,2}\naput{\mymatrix{0\\\mkern-5mu\mathbf{1}_{G_2\mkern-4mu}}}
\ncline{1,3}{2,3}\naput{\mymatrix{0\\\mkern-5mu\mathbf{1}_{F_2\mkern-4mu}}}
\end{psmatrix} \]

\end{document}

enter image description here

答案3

这是一个利用包的机制amscd以及包bsmallmatrix提供的环境的解决方案mathtools。

enter image description here

\documentclass{article}  
\usepackage{mathtools,amscd}
\begin{document}
\[\begin{CD}
F_2 @>\phi_2>> G_2 @>\phi_2>> F_2 \\
@VV{\begin{psmallmatrix}0\\1^{}_{F_2}\end{psmallmatrix}}V
@VV{\begin{psmallmatrix}0\\1^{}_{G_2}\end{psmallmatrix}}V
@VV{\begin{psmallmatrix}0\\1^{}_{F_2}\end{psmallmatrix}}V \\
G_1\oplus F_2 
@>{\smash[t]{\,\begin{psmallmatrix}
   -\psi_1 & 0 \\ g & \phi_2
   \end{psmallmatrix}}}>> 
F_1\oplus G_2 
@>{\smash[t]{\,\,\begin{psmallmatrix}
   -\phi_1 & 0 \\ f & \psi_2
   \end{psmallmatrix}}}>> 
G_1\oplus F_2
\end{CD}\]
\end{document}

答案4

使用 tikz 的答案：

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usetikzlibrary{positioning}

\begin{document}
   \begin{tikzpicture}
      \node (A) {$F_2$};
      \node[right=3cm of A] (B) {$G_2$};
      \node[right=3cm of B] (C) {$F_2$};
      \node[below=2cm of A] (D) {$G_1\oplus F_2$};
      \node[below=2cm of B] (E) {$F_1\oplus G_2$};
      \node[below=2cm of C] (F) {$G_1 \oplus F_2$};
      \draw[->] (A)--(B) node[midway, above] {$\phi_2$};
      \draw[->] (B)--(C) node[midway, above] {$\psi_2$};
      \draw[->] (D)--(E) node[midway, above,font=\small] {$\begin{pmatrix}-\psi_1 & 0\\ g& \phi_2\end{pmatrix}$};
      \draw[->] (E)--(F) node[midway, above,font=\small] {$\begin{pmatrix}-\phi_1 & 0\\f& \psi_2\end{pmatrix}$};
      \draw[->] (A)--(D) node[midway, right,font=\small] {$\begin{pmatrix}0\\1_{F_2}\end{pmatrix}$};
      \draw[->] (B)--(E) node[midway, right,font=\small] {$\begin{pmatrix}0\\1_{G_2}\end{pmatrix}$};
      \draw[->] (C)--(F) node[midway, right,font=\small] {$\begin{pmatrix}0\\1_{F_2}\end{pmatrix}$};

   \end{tikzpicture}

\end{document}

我建议使用 tikz，因为它具有非常先进的用户控制功能，并且在您学习基础知识之后可以在任何地方使用它。

输出：

enter image description here

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