如何在这样的矩阵中画一个圆圈？

Question

我在一本书中看到了这样的矩阵。我可以使用纯 latex 命令创建它吗？还是需要借助 Photoshop 之类的工具来提供帮助？

---

更新：我创建了没有圆的方程，如下所示：

\documentclass[a4paper,12pt,hidelinks]{article}
\usepackage{mathtools}
\begin{document}
\title{Title of the doc}
\author{me}
\date{\today}
\maketitle
\section{Example}

\begin{equation*}
\begin{vmatrix*}[c]
a_{11} & a_{12} & \cdots & a_{1n} \\
& a_{22} & \cdots & a_{2n} \\
&& \ddots & \vdots \\
&&& a_{nn}
\end{vmatrix*} =
\begin{vmatrix*}[c]
a_{11} &&& \\
a_{21} & a_{22} && \\
\vdots & \vdots & \ddots & \\
a_{n1} & a_{n2} & \cdots & a_{nn}
\end{vmatrix*} =
a_{11}a_{22} \dots a_{nn}
\end{equation*}

\end{document}

Answer 1

运行xelatex

\documentclass{article}
\usepackage{amsmath}
\usepackage{pstricks}
\begin{document}
\[
  \begin{vmatrix}
    a_{11} & a_{12} & \cdots & a_{1n} \\
           & a_{22} & \cdots & a_{2n} \\
      \psellipse[rot=45](0.5,0)(0.3,0.6) & & \ddots & \vdots \\
      & & & a_{nn}
    \end{vmatrix}
    =
    \begin{vmatrix}
    a_{11} &  &  &  \\
    a_{21} & a_{22} &  & \psellipse[rot=45](-0.5,0.1)(0.3,0.6) \\
    \vdots & \vdots & \ddots  & \\
    a_{n1} & a_{n1} & \cdots & a_{nn}
    \end{vmatrix}
    = a_{11}\, a_{22}\cdots a_{nn}
\]
\end{document}

和包相同tikz

\[
\begin{vmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
& a_{22} & \cdots & a_{2n} \\
\tikz[overlay]\draw (0.5,0) circle [x radius=3mm,y radius=6mm,rotate=45]; 
  & & \ddots & 
\vdots \\
& & & a_{nn}
\end{vmatrix}
=
\begin{vmatrix}
a_{11} &  &  &  \\
a_{21} & a_{22} &  & 
   \tikz[overlay]\draw (-0.5,0.1) circle [x radius=3mm,y radius=6mm,rotate=45]; \\
\vdots & \vdots & \ddots  & \\
a_{n1} & a_{n1} & \cdots & a_{nn}
\end{vmatrix}
= a_{11}\, a_{22}\cdots a_{nn}
\]

Answer 2

这是使用 tikzmark 实现此目的的可能方法。(更新：椭圆的旋转角度不再硬编码。）

\documentclass[a4paper,12pt,hidelinks]{article}
\usepackage{mathtools}
\usepackage{tikz}
\usetikzlibrary{tikzmark,fit,shapes.geometric,calc}
\begin{document}
\title{Title of the doc}
\author{me}
\date{\today}
\maketitle
\section{Example}

\begin{equation*}
\begin{vmatrix*}[c]
a_{11} & a_{12} & \cdots & a_{1n} \\
& a_{22} & \cdots & a_{2n} \\
\tikzmark{m1}&& \ddots & \vdots \\
&\tikzmark{m2}&& a_{nn}
\end{vmatrix*} =
\begin{vmatrix*}[c]
a_{11} &&\tikzmark{m3}& \\
a_{21} & a_{22} &&\tikzmark{m4} \\
\vdots & \vdots & \ddots & \\
a_{n1} & a_{n2} & \cdots & a_{nn}
\end{vmatrix*} =
a_{11}a_{22} \dots a_{nn}
\end{equation*}
\begin{tikzpicture}[overlay,remember picture]
\path let \p1=($(pic cs:m2)-(pic cs:m1)$),\n1={atan2(\y1,\x1)} in
node[ellipse,fit=(pic cs:m1)(pic cs:m2),draw,rotate fit=\n1,inner sep=0pt,
yshift=4pt]{};
\path let \p1=($(pic cs:m4)-(pic cs:m3)$),\n1={atan2(\y1,\x1)} in
node[ellipse,fit=(pic cs:m3)(pic cs:m4),draw,rotate fit=\n1,inner sep=0pt]{};
\end{tikzpicture}
\end{document}