突出显示矩阵中的元素并用箭头将它们与其他参数链接起来

Question

我想突出显示矩阵中的某些元素，并用箭头将它们链接到矩阵侧给出的定义（如下图所示）。我知道使用 TikZ 可以突出显示矩阵中的元素，但是是否可以在侧面使用框、箭头和文本（数学符号）？最简单的方法是什么？不使用 TikZ 可以做到这一点吗？

这是我目前的代码：

\documentclass[twocolumn]{article}
\usepackage{mathtools}
\mathtoolsset{showonlyrefs}

\begin{document}
\begin{eqnarray}
    \mathbf{N} &=& \begin{pmatrix}
        n_{11} & 0 & n_{13} & n_{14} \\
        n_{21} & n_{22} & n_{23} & n_{24} \\
        n_{31} & n_{32} & n_{33} & 0 \\
        n_{41} & n_{42} & n_{43} & n_{44} 
    \end{pmatrix}\\
     &=& \begin{pmatrix}
        \sqrt{\beta_x} & 0 & n_{13} & n_{14} \\
        -\frac{\alpha_x}{\sqrt{\beta_x}} & n_{22} & n_{23} & n_{24} \\
        n_{31} & n_{32} & \sqrt{\beta_y} & 0 \\
        n_{41} & n_{42} & -\frac{\alpha_y}{\sqrt{\beta_y}} & n_{44} 
    \end{pmatrix}
\end{eqnarray}

\end{document}

感谢您的帮助！

Answer 1

这是用 TikZ 做的，请原谅我。

问题在于您要绘制的内容对于双列文档中的一列来说太大。

这里有两种可能的解决方案：在一列中，描述的位置不同，或者在两列中。

\documentclass[twocolumn]{article}
\usepackage{mwe}% <--- for testing purpose only
\usepackage{cuted}
\usepackage{tikz}
\usetikzlibrary{matrix, fit}
\usetikzlibrary{arrows.meta}
\tikzset{mymatrixstyle/.style={matrix of math nodes,
        ampersand replacement=\&,
        left delimiter=(,
        right delimiter=), 
        inner sep=0pt,
        outer sep=0pt,
        row sep=2pt, column sep=10pt},
        myarrow/.style={-{Straight Barb[angle=60:3pt 3]}}}
\usepackage{mathtools}
\mathtoolsset{showonlyrefs}

\begin{document} 
\blindtext % <--- for testing purpose only

In one column:
%\begin{eqnarray} see https://tex.stackexchange.com/a/197/101651
\begin{align}
    \mathbf{N} &= \begin{pmatrix}
        n_{11} & 0 & n_{13} & n_{14} \\
        n_{21} & n_{22} & n_{23} & n_{24} \\
        n_{31} & n_{32} & n_{33} & 0 \\
        n_{41} & n_{42} & n_{43} & n_{44} 
    \end{pmatrix}\\
     &= \begin{tikzpicture}[baseline]
        \matrix[mymatrixstyle] (mymatr) {
        \sqrt{\beta_x} \& 0 \& n_{13} \& n_{14} \&[-7pt]\\
        -\dfrac{\alpha_x}{\sqrt{\beta_x}} \& n_{22} \& n_{23} \& n_{24} \\
        n_{31} \& n_{32} \& \sqrt{\beta_y} \& 0 \\
        n_{41} \& n_{42} \& -\dfrac{\alpha_y}{\sqrt{\beta_y}} \& n_{44}\\};
        \node[draw, fit=(mymatr-3-1)(mymatr-3-2)] (n3132) {};
        \node[draw, fit=(mymatr-4-1)(mymatr-4-2)] (n4142) {};
        \node[draw, fit=(mymatr-1-3)(mymatr-1-4)] (n1314) {};
        \node[draw, fit=(mymatr-2-3)(mymatr-2-4)] (n2324) {};
        \draw[myarrow, overlay] (n3132) -- ++(-1.8,0) -| +(0,-1.6) node[anchor=north] {$\zeta_y=n_{31}+in_{32}$};
        \draw[myarrow] (n4142) -- +(0,-1.8) node[anchor=north] {$\tilde{\zeta}_y=n_{41}-in_{42}$};
        \draw[myarrow, overlay] (n1314) -- ++(2,0) -|  +(0,-3.6) node[anchor=20] {$\zeta_y=n_{13}-in_{14}$};
        \draw[myarrow, overlay] (n2324) -- ++(1.4,0) -|  +(0,-2.1) node[anchor=20] {$\tilde{\zeta}_y=n_{23}-in_{24}$};
    \end{tikzpicture}        
\end{align}

\blindtext[7] % <--- for testing purpose only

In two columns:

\begin{strip}
\begin{align}
    \mathbf{N} &= \begin{pmatrix}
        n_{11} & 0 & n_{13} & n_{14} \\
        n_{21} & n_{22} & n_{23} & n_{24} \\
        n_{31} & n_{32} & n_{33} & 0 \\
        n_{41} & n_{42} & n_{43} & n_{44} 
    \end{pmatrix}\\
     &= \begin{tikzpicture}[baseline]
        \matrix[mymatrixstyle] (mymatr) {
        \sqrt{\beta_x} \& 0 \& n_{13} \& n_{14} \&[-7pt]\\
        -\dfrac{\alpha_x}{\sqrt{\beta_x}} \& n_{22} \& n_{23} \& n_{24} \\
        n_{31} \& n_{32} \& \sqrt{\beta_y} \& 0 \\
        n_{41} \& n_{42} \& -\dfrac{\alpha_y}{\sqrt{\beta_y}} \& n_{44}\\};
        \node[draw, fit=(mymatr-3-1)(mymatr-3-2)] (n3132) {};
        \node[draw, fit=(mymatr-4-1)(mymatr-4-2)] (n4142) {};
        \node[draw, fit=(mymatr-1-3)(mymatr-1-4)] (n1314) {};
        \node[draw, fit=(mymatr-2-3)(mymatr-2-4)] (n2324) {};
        \draw[myarrow, overlay] (n3132) -- +(-1.8,0) node[anchor=east] {$\zeta_y=n_{31}+in_{32}$};
        \draw[myarrow, overlay] (n4142) -- +(-1.8,0) node[anchor=east] {$\tilde{\zeta}_y=n_{41}-in_{42}$};
        \draw[myarrow, overlay] (n1314) -- +(1.8,0) node[anchor=west] {$\zeta_y=n_{13}-in_{14}$};
        \draw[myarrow, overlay] (n2324) -- +(1.8,0) node[anchor=west] {$\tilde{\zeta}_y=n_{23}-in_{24}$};
    \end{tikzpicture}        
\end{align}
\end{strip}

\blindtext[7] % <--- for testing purpose only
\end{document}

题外话：不要使用eqnarray，原因请参见此处：https://tex.stackexchange.com/a/197/101651