tikzで行列の積を表現してみる

行列の積の成分計算を表す図をtikzで作成してみました。元ネタは佐武線形代数です。
画像は次の通り。

LaTeXのコードは次のようになりました。
行列の外の括弧を表現するのにdecorations.pathreplacingライブラリを，
行列を上部で揃えるのにpositioningライブラリを使っています．
色付けはbackgroundsライブラリを使い，scope環境にon background layerオプションを付けて文字の背後に色を付けるようにしました．

\documentclass[a4paper,dvipdfmx,uplatex]{jsarticle}

\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{matrix,backgrounds,fit,positioning}

\begin{document}
\begin{equation*}
\begin{tikzpicture}[every left delimiter/.style={xshift=1ex},every right delimiter/.style={xshift=-1ex}]
%
\matrix(A)[matrix of math nodes,nodes in empty cells,
 ampersand replacement=\&,
 left delimiter={[},right delimiter={]},
 inner sep=0.8ex,
 ]
 {
 \phantom{b_{11}}\&\hphantom{\dotsb}\&\phantom{\dotsb}\&a_{1j}\&\phantom{b_{1n}}\\
 \phantom{a_{11}}\&\&\&a_{2j}\&\phantom{a_{1n}}\\
 \phantom{\mathstrut}\&\&\&\phantom{\mathstrut}\&\\
 \phantom{\mathstrut}\&\&\&\phantom{\mathstrut}\&\\ 
 \phantom{a_{11}}\&\&\&a_{mj}\&\phantom{a_{1n}}\\
 };
 \draw[line width=1pt,line cap=round,dash pattern=on 0pt off 4\pgflinewidth](A-3-4.north)--(A-4-4.south);
 \draw[decorate,decoration={brace,amplitude=5}]
($(A-1-1.north west)+(-0.5ex,1.5ex)$)--($(A-1-5.north east)+(0.5ex,1.5ex)$)
 node[midway,yshift=2.5ex]{$n$};
 \draw[decorate,decoration={brace,mirror,amplitude=5}]
($(A-1-1.north west)+(-1.8ex,0.2ex)$)--($(A-5-1.south west)+(-1.8ex,-0.2ex)$)
 node[midway,xshift=-2.5ex]{$m$};
 \begin{scope}[on background layer]
 \fill[gray!40,rounded corners](A-1-4.north west) rectangle (A-5-4.south east);
 \end{scope} 

 \matrix(B)[matrix of math nodes,nodes in empty cells,
 ampersand replacement=\&,left delimiter={[},right delimiter={]},inner sep=0.8ex,
 left=0.8cm of A.north west,
 anchor=north east]
 {
 \phantom{b_{11}}\&\&\&\&\phantom{b_{11}}\\
 b_{h1}\&b_{h2}\&\vphantom{b_{h1}}\phantom{\dotsb}\&\phantom{\dotsb}\vphantom{b_{h1}}\&b_{h m}\\
 \phantom{b_{11}}\&\&\&\&\\
 \phantom{b_{11}}\&\&\&\&\\
 };
 \node[inner sep=0pt,fit=(B-2-3)(B-2-4)](fit1){};
 \node[baseline=(fit1.base)]at (fit1){$\dotsb\dotsb$};
 \draw[decorate,decoration={brace,amplitude=5}]
($(B-1-1.north west)+(-0.5ex,1.5ex)$)--($(B-1-5.north east)+(0.5ex,1.5ex)$)
 node[midway,yshift=2.5ex]{$m$};
 \draw[decorate,decoration={brace,mirror,amplitude=5}]
($(B-1-1.north west)+(-1.8ex,0.2ex)$)--($(B-4-1.south west)+(-1.8ex,-0.2ex)$)
 node[midway,xshift=-2.5ex]{$l$};
 \begin{scope}[on background layer]
 \fill[gray!40,rounded corners](B-2-1.south west) rectangle (B-2-5.north east);
 \end{scope} 

\matrix(BA)[matrix of math nodes,nodes in empty cells,
 ampersand replacement=\&,
 left delimiter={[},right delimiter={]},
 inner sep=0.8ex,
right=1.4cm of A.north east,
anchor=north west
]
 {
 \phantom{b_{11}}\&\phantom{\dotsb}\&\phantom{\dotsb}\&\phantom{b_{hj}}\&\phantom{b_{11}}\\
 \phantom{c_{11}}\&\phantom{c_{11}}\&\&\node[fill=gray!40,rounded corners]{c _{hj}};\&\phantom{c_{11}}\\
 \phantom{b_{11}}\&\&\&\phantom{c_{11}}\&\\
 \phantom{b_{11}}\&\&\&\phantom{b_{11}}\&\phantom{b_{11}}\\
 };
 \draw[decorate,decoration={brace,amplitude=5}]
($(BA-1-1.north west)+(-0.5ex,1.5ex)$)--($(BA-1-5.north east)+(0.5ex,1.5ex)$)
 node[midway,yshift=2.5ex]{$n$};
 \draw[decorate,decoration={brace,mirror,amplitude=5}]
($(BA-1-1.north west)+(-1.8ex,0.2ex)$)--($(BA-4-1.south west)+(-1.8ex,-0.2ex)$)
 node[midway,xshift=-2.5ex]{$l$};
\begin{scope}[on background layer]
 \draw[line width=1pt,line cap=round,dash pattern=on 0 pt off 4\pgflinewidth]
(BA-1-4.north)--(BA-4-4.south) (BA-2-1.west)--(BA-2-5.east);
\end{scope}
\node at($(A.east)+(10pt,15pt)$){$=$};
\node[below=0.5cm of A](A2){$A$};
\node(B2)at(B |- A2){$B$};
\node(BA2)at(BA |- A2){$BA$};
\draw[line width=1pt,line cap=round,dash pattern=on 0 pt off 4\pgflinewidth](B)--(B2) (A)--(A2) (BA)--(BA2);
\end{tikzpicture}
\end{equation*}
\end{document}