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%
% nilpotent.tex -- Produkt nilpotenter Matrizen
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math}
\usepackage[many]{tcolorbox}
\begin{document}
\def\skala{1}
\newtcbox{\myboxA}{blank,boxsep=0mm,
clip upper,minipage,
width=31.0mm,height=17.0mm,nobeforeafter,
borderline={0.0pt}{0.0pt}{white},
}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\def\cx{1.8}
\def\cy{1.2}
\draw[line width=0.3pt] (-3,2.5) -- (6,2.5);
\begin{scope}[xshift=-4cm]
\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
\fill[color=red!30] (0.5,3) -- (3,0.5) -- (3,3) -- cycle;
\draw (0,0) rectangle (3,3);
\draw (0,3) -- (3,0);
\node at ({\cx+0.5*0.5},{\cy+0.5*0.5}) [rotate=-45] {$k$};
\draw[color=blue,line width=1.4pt] (0,2.5) -- (1.0,2.5);
\draw[color=red,line width=1.4pt] (1.0,2.5) -- (3,2.5);
\node at (1,1) {$B$};
\node at (-0.3,2.5) [left] {$i$};
\node at (1,2.5) [above right] {$i+k$};
\end{scope}
\node at (-0.5,1.5) {$\mathstrut\cdot\mathstrut$};
\begin{scope}
\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
\fill[color=red!30] (1.0,3) -- (3,1.0) -- (3,3) -- cycle;
\draw (0,0) rectangle (3,3);
\draw (0,3) -- (3,0);
\node at ({\cx+1.0*0.5},{\cy+1.0*0.5}) [rotate=-45] {$l$};
\draw[color=red,line width=1.4pt] (2,3)--(2,2);
\draw[color=blue,line width=1.4pt] (2,2)--(2,0);
\node at (1,1) {$C$};
\node at (2,3) [above] {$j$};
\node at (2,2) [above right] {$j-l$};
\end{scope}
\node at (3.5,1.5) {$\mathstrut=\mathstrut$};
\begin{scope}[xshift=4cm]
\node at (1.5,1.53) {$\left(\myboxA{}\right)$};
\fill[color=red!30] (1.5,3) -- (3,1.5) -- (3,3) -- cycle;
\draw (0,0) rectangle (3,3);
\draw (0,3) -- (3,0);
\node at ({\cx+1.5*0.5},{\cy+1.5*0.5}) [rotate=-45] {$k+l$};
\fill[color=red!50!blue] (2,2.5) circle[radius=0.1];
\draw[line width=0.3pt] (2,3) -- (2,2.5);
\node at (2,3) [above] {$j$};
\node at (1,1) {$D$};
\end{scope}
\end{tikzpicture}
\end{document}
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