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附录

tag-icon • tag-icon tikz-matrix
附录

我想在 tikz 中实现下一个结果： 在此处输入图片描述

但是，我只能绘制矩阵，而不能进行它们之间的数学运算，即点积和等号（括号的高度相同是一个优点）。下面我附上了我的部分代码以及我目前所取得的进展。

任何帮助将非常感激

谢谢

\documentclass[usenames,dvipsnames]{beamer}
\usepackage{tikz}
    \usetikzlibrary{arrows.meta}
    \usetikzlibrary{decorations.pathreplacing}
    \usetikzlibrary{fit, calc, matrix, positioning, arrows.meta, intersections, through, backgrounds, patterns}
\usepackage{pgfplots}
    \pgfplotsset{compat = newest}
    \pgfplotsset{overwrite option/.style args={#1 with #2}{#1=#2,#1/.code=}}


\begin{frame}{MATRIX MULTIPLICATION}
    More graphically:
    
    \begin{tikzpicture}
    \scriptsize
        \matrix (m)[
        matrix of math nodes,
        nodes in empty cells,
        %minimum width=width("998888"),
        left delimiter=(,
        right delimiter=)
        ] {
        a_{11} && \cdots && a_{1k} && \cdots &&  a_{1n} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        a_{i1} && \cdots && a_{ik} && \cdots &&  a_{in} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        a_{m1} && \cdots && a_{mk} && \cdots &&  a_{mn} \\
        } ;
        
        \draw (m-3-1.south west) rectangle (m-3-5.north east);
        
    \begin{scope}[xshift=95pt]
        
        \matrix (m)[
        matrix of math nodes,
        nodes in empty cells,
        %minimum width=width("998888"),
        left delimiter=(,
        right delimiter=)
        ] {
        b_{11} && \cdots && b_{1j} && \cdots &&  b_{1p} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        b_{k1} && \cdots && b_{kj} && \cdots &&  b_{kp} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        b_{n1} && \cdots && b_{nj} && \cdots &&  b_{np} \\
        } ;
        
        \draw (m-5-3.south west) rectangle (m-1-3.north east);
    \end{scope}
    \begin{scope}[xshift=200pt]
        
        \matrix (m)[
        matrix of math nodes,
        nodes in empty cells,
        %minimum width=width("998888"),
        left delimiter=(,
        right delimiter=)
        ] {
        c_{11} && \cdots && c_{1j} && \cdots &&  c_{1p} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        c_{i1} && \cdots && c_{ij} && \cdots &&  c_{ip} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        c_{m1} && \cdots && c_{mj} && \cdots &&  c_{mp} \\
        } ;
        
        \draw (m-3-3.south west) rectangle (m-3-3.north east);
    \end{scope}    
    \end{tikzpicture}
\end{frame}

在此处输入图片描述

答案1

首先，我会使用positioning库将矩阵彼此相邻放置，然后无需找出正确的xshift。 （您也可以这样做\matrix (m2) at (95pt,0) ...而不是scope。）

命名矩阵m和m2后m3，您可以例如执行

\path (m) -- node {$\cdot$} (m2)
      (m2) -- node {$=$} (m3);

将符号置于它们中间。

在此处输入图片描述

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning, matrix}
\begin{document}
\begin{tikzpicture}
    \scriptsize
        \matrix (m)[
        matrix of math nodes,
        nodes in empty cells,
        %minimum width=width("998888"),
        left delimiter=(,
        right delimiter=)
        ] {
        a_{11} && \cdots && a_{1k} && \cdots &&  a_{1n} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        a_{i1} && \cdots && a_{ik} && \cdots &&  a_{in} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        a_{m1} && \cdots && a_{mk} && \cdots &&  a_{mn} \\
        } ;
        
        \draw (m-3-1.south west) rectangle (m-3-5.north east);
        

        
        \matrix (m2) [
        matrix of math nodes,
        nodes in empty cells,
        %minimum width=width("998888"),
        left delimiter=(,
        right delimiter=),
        right=of m
        ] {
        b_{11} && \cdots && b_{1j} && \cdots &&  b_{1p} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        b_{k1} && \cdots && b_{kj} && \cdots &&  b_{kp} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        b_{n1} && \cdots && b_{nj} && \cdots &&  b_{np} \\
        } ;
        
        \draw (m-5-3.south west) rectangle (m-1-3.north east);

        
        \matrix (m3)[
        matrix of math nodes,
        nodes in empty cells,
        %minimum width=width("998888"),
        left delimiter=(,
        right delimiter=),
        right=of m2
        ] {
        c_{11} && \cdots && c_{1j} && \cdots &&  c_{1p} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        c_{i1} && \cdots && c_{ij} && \cdots &&  c_{ip} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        c_{m1} && \cdots && c_{mj} && \cdots &&  c_{mp} \\
        } ;
        
        \draw (m-3-3.south west) rectangle (m-3-3.north east);

        \path (m) -- node {$\cdot$} (m2)
              (m2) -- node {$=$} (m3);
    \end{tikzpicture}
\end{document}

附录

请注意，beamer您不能直接使用矩阵，您需要一个fragile框架或使用ampersand replacement，例如在 beamer 中使用 tikz 矩阵时出现“单个 & 符号与错误的 catcode 一起使用”错误

下面我制作了框架fragile。我还制作了一种新样式pmat，并将其应用于所有矩阵，并进行了一些修改，以便它们实际上适合框架。

在此处输入图片描述

\documentclass[usenames,dvipsnames]{beamer}
\usepackage{tikz}
    \usetikzlibrary{arrows.meta}
    \usetikzlibrary{decorations.pathreplacing}
    \usetikzlibrary{fit, calc, matrix, positioning, arrows.meta, intersections, through, backgrounds, patterns}
\usepackage{pgfplots}
    \pgfplotsset{compat = newest}
    \pgfplotsset{overwrite option/.style args={#1 with #2}{#1=#2,#1/.code=}}
\begin{document}

\begin{frame}[fragile]{MATRIX MULTIPLICATION}
    More graphically:
    
 \begin{tikzpicture}[
    pmat/.style={
       matrix of math nodes,
       nodes={font=\footnotesize\strut, inner sep=1.5pt},
       left delimiter=(,
       right delimiter=),
       }
       ]

        \matrix (m)[pmat] {
        a_{11} && \cdots && a_{1k} && \cdots &&  a_{1n} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        a_{i1} && \cdots && a_{ik} && \cdots &&  a_{in} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        a_{m1} && \cdots && a_{mk} && \cdots &&  a_{mn} \\
        } ;
        
        \draw (m-3-1.south west) rectangle (m-3-5.north east);
        
        
        \matrix (m2) [pmat,right=of m] {
        b_{11} && \cdots && b_{1j} && \cdots &&  b_{1p} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        b_{k1} && \cdots && b_{kj} && \cdots &&  b_{kp} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        b_{n1} && \cdots && b_{nj} && \cdots &&  b_{np} \\
        } ;
        
        \draw (m-5-3.south west) rectangle (m-1-3.north east);

        
        \matrix (m3)[pmat,right=of m2] {
        c_{11} && \cdots && c_{1j} && \cdots &&  c_{1p} \\
        \vdots &&        && \vdots &&        &&\vdots  \\
        c_{i1} && \cdots && c_{ij} && \cdots &&  c_{ip} \\
        \vdots &&        && \vdots &&        && \vdots  \\
        c_{m1} && \cdots && c_{mj} && \cdots &&  c_{mp} \\
        } ;
        
        \draw (m-3-3.south west) rectangle (m-3-3.north east);

        \path (m) -- node {$\cdot$} (m2)
              (m2) -- node {$=$} (m3);
    \end{tikzpicture}
\end{frame}
\end{document}

答案2

在此处输入图片描述

使用\vphantom{b_{ij}}第一个和最后一个矩阵中每行开头的变量：

\documentclass[usenames,dvipsnames]{beamer}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,
                backgrounds, 
                calc, 
                decorations.pathreplacing,
                fit, 
                intersections, 
                matrix, 
                positioning, patterns,
                through
                }

\begin{document}
\begin{frame}[fragile]
\frametitle{MATRIX MULTIPLICATION}

    More graphically:
    
\[
    \begin{tikzpicture}[
every matrix/.style = {matrix of math nodes,
                       nodes in empty cells,
                       nodes = {inner sep=2pt, font=\scriptsize},
                       left delimiter=(,
                       right delimiter=),
                       inner sep=0pt
                       },
                        ]    
\matrix (m1)
    {
\vphantom{b_{ij}}
    a_{11} & \cdots & a_{1k} & \cdots &  a_{1n} \\
    \vdots &        & \vdots &        & \vdots  \\
\vphantom{b_{ij}}
    a_{i1} & \cdots & a_{ik} & \cdots &  a_{in} \\
    \vdots &        & \vdots &        & \vdots  \\
\vphantom{b_{ij}}
    a_{m1} & \cdots & a_{mk} & \cdots &  a_{mn} \\
    } ;
\draw (m1-3-1.south west) rectangle (m1-3-5.north east);
\node (m1a) [right=2mm of m1] {$\cdot$};
\matrix (m2)[right=2mm of m1a] 
    {
    b_{11} & \cdots & b_{1j} & \cdots &  b_{1p} \\
    \vdots &        & \vdots &        & \vdots  \\
    b_{k1} & \cdots & b_{kj} & \cdots &  b_{kp} \\
    \vdots &        & \vdots &        & \vdots  \\
    b_{n1} & \cdots & b_{nj} & \cdots &  b_{np} \\
    } ;
\draw (m2-5-3.south west) rectangle (m2-1-3.north east);
\node (m2a) [right=2mm of m2] {$=$};
\matrix (m3) [right=2mm of m2a] 
    {
\vphantom{b_{ij}}
    c_{11} & \cdots & c_{1j} & \cdots &  c_{1p} \\
    \vdots &        & \vdots &        &\vdots  \\
\vphantom{b_{ij}}
    c_{i1} & \cdots & c_{ij} & \cdots &  c_{ip} \\
    \vdots &        & \vdots &        & \vdots  \\
\vphantom{b_{ij}}
    c_{m1} & \cdots & c_{mj} & \cdots &  c_{mp} \\
    } ;
\draw (m3-3-3.south west) rectangle (m3-3-3.north east);
    \end{tikzpicture}
\]
\end{frame}
\end{document}

答案3

您可以使用{pNiceMatrix}of来实现这一点。此环境与ofnicematrix类似，但在数组的单元格下创建 PGF/Tikz 节点。使用这些节点可以轻松使用 Tikz 绘制矩形。{pmatrix}amsmath

\documentclass[usenames,dvipsnames]{beamer}
\usepackage{tikz}
\usepackage{nicematrix}

\begin{document}

\begin{frame}[fragile]{MATRIX MULTIPLICATION}
    More graphically:

\NiceMatrixOptions{small,create-large-nodes,columns-width=4mm}

$\begin{pNiceArray}{ccccc<{\vphantom{b_{np}}}}
a_{11} & \cdots & a_{1j} & \cdots &  a_{1p} \\
\vdots &        & \vdots &        &\vdots  \\
a_{i1} & \cdots & a_{ij} & \cdots &  a_{ip} \\
\vdots &        & \vdots &        & \vdots  \\
a_{m1} & \cdots & a_{mj} & \cdots &  a_{mp} 
\CodeAfter
\tikz \draw (3-1-large.south west) rectangle (3-5-large.north east);
\end{pNiceArray}
\cdot
\begin{pNiceArray}{ccccc}
b_{11} & \cdots & b_{1j} & \cdots &  b_{1p} \\
\vdots &        & \vdots &        &\vdots  \\
b_{k1} & \cdots & b_{kj} & \cdots &  b_{kp} \\
\vdots &        & \vdots &        & \vdots  \\
b_{n1} & \cdots & b_{nj} & \cdots &  b_{np} 
\CodeAfter
\tikz \draw (5-3-large.south west) rectangle (1-3-large.north east);
\end{pNiceArray}
=
\begin{pNiceArray}{ccccc<{\vphantom{b_{np}}}}
c_{11} & \cdots & c_{1j} & \cdots &  c_{1p} \\
\vdots &        & \vdots &        &\vdots  \\
c_{i1} & \cdots & c_{ij} & \cdots &  c_{ip} \\
\vdots &        & \vdots &        & \vdots  \\
c_{m1} & \cdots & c_{mj} & \cdots &  c_{mp} 
\CodeAfter
\tikz \draw (3-3-large.south west) rectangle (3-3-large.north east);
\end{pNiceArray}$
\end{frame}

\end{document}

上述代码的输出

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