How can I draw those line joining matrix

Question

I'm trying to draw something like this :

I have created matrix normally, from here :

\begin{bmatrix}
x_{11}       & x_{12} & x_{13} & \dots & x_{1n} \\
x_{21}       & x_{22} & x_{23} & \dots & x_{2n} \\
\hdotsfor{5} \\
x_{d1}       & x_{d2} & x_{d3} & \dots & x_{dn}
\end{bmatrix}

But it doesn't give that 3D feeling and how can I create the those line between those matrices.

Answer 1

Welcome! You can use tikz-3dplot to install a view and the 3d library of TikZ, which automatically gets loaded, to project the matrices on some planes.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{65}{60}
\begin{tikzpicture}[tdplot_main_coords]
\begin{scope}[canvas is xz plane at y=2,transform shape]
 \node[inner xsep=-3pt,inner ysep=-0.3pt] (mat1){$\displaystyle
  \begin{bmatrix}
  x_{11}       & x_{12} \\
  x_{21}       & x_{22}  \\
  \end{bmatrix}$};
\end{scope}
%
\begin{scope}[canvas is xz plane at y=0,transform shape]
 \node[inner xsep=-4pt,inner ysep=-0.3pt] (mat2){$\displaystyle
  \begin{bmatrix}
  x_{11}       & x_{12} & x_{13} & \dots & x_{1n} \\
  x_{21}       & x_{22} & x_{23} & \dots & x_{2n} \\
  \hdotsfor{5} \\
  x_{d1}       & x_{d2} & x_{d3} & \dots & x_{dn}
  \end{bmatrix}$};
\end{scope}
\foreach \Y in {south,north} {\foreach \X in {west,east}
{\draw (mat1.\Y\space\X)  -- (mat2.\Y\space\X);}}
\end{tikzpicture}
\end{document}

One can also install the background pattern.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{backgrounds}
\begin{document}
\tdplotsetmaincoords{65}{60}
\begin{tikzpicture}[tdplot_main_coords]
\begin{scope}[canvas is xz plane at y=2,transform shape]
 \node[inner xsep=-3pt,inner ysep=-0.3pt] (mat1){$\displaystyle
  \begin{bmatrix}
  x_{11}       & x_{12} \\
  x_{21}       & x_{22}  \\
  \end{bmatrix}$};
\end{scope}
%
\begin{scope}[canvas is xz plane at y=0,transform shape]
 \node[inner xsep=-4pt,inner ysep=-0.3pt] (mat2){$\displaystyle
  \begin{bmatrix}
  x_{11}       & x_{12} & x_{13} & x_{14} \\
  x_{21}       & x_{22} & x_{23} & x_{24} \\
  x_{31}       & x_{32} & x_{33} & x_{34} \\
  x_{41}       & x_{42} & x_{43} & x_{44} \\
  \end{bmatrix}$};
\end{scope}
%
\begin{scope}[on background layer]
 \foreach \Y in {south,north} {\foreach \X in {west,east}
 {\draw (mat1.\Y\space\X)  -- (mat2.\Y\space\X);}}
 \foreach \X in {1,2}
 {\fill[blue!20] (mat\X.west)  -- (mat\X.east) -- (mat\X.south east) 
  -- (mat\X.south) -- (mat\X.north) -- (mat\X.north west) -- cycle; }
\end{scope} 
\end{tikzpicture}
\end{document}

You seem to have problems with installing tikz-3dplot. While there should not be a problem, here is a possible workaround. Save this file as tikzlibrary3dtools.code.tex in the same directory as the file you are compiling. Then this should work, too:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{backgrounds,3d,3dtools}
\begin{document}
\begin{tikzpicture}[3d/install view={phi=70,psi=0,theta=70}]
\begin{scope}[canvas is xz plane at y=2,transform shape]
 \node[inner xsep=-3pt,inner ysep=-0.3pt] (mat1){$\displaystyle
  \begin{bmatrix}
  x_{11}       & x_{12} \\
  x_{21}       & x_{22}  \\
  \end{bmatrix}$};
\end{scope}
%
\begin{scope}[canvas is xz plane at y=0,transform shape]
 \node[inner xsep=-4pt,inner ysep=-0.3pt] (mat2){$\displaystyle
  \begin{bmatrix}
  x_{11}       & x_{12} & x_{13} & x_{14} \\
  x_{21}       & x_{22} & x_{23} & x_{24} \\
  x_{31}       & x_{32} & x_{33} & x_{34} \\
  x_{41}       & x_{42} & x_{43} & x_{44} \\
  \end{bmatrix}$};
\end{scope}
%
\begin{scope}[on background layer]
 \foreach \Y in {south,north} {\foreach \X in {west,east}
 {\draw (mat1.\Y\space\X)  -- (mat2.\Y\space\X);}}
 \foreach \X in {1,2}
 {\fill[blue!20] (mat\X.west)  -- (mat\X.east) -- (mat\X.south east) 
  -- (mat\X.south) -- (mat\X.north) -- (mat\X.north west) -- cycle; }
\end{scope} 
\end{tikzpicture}
\end{document}

Notice that the conventions for the angles may change in future revisions of the library. The problem is that different packages follow different conventions, which applies to e.g. tikz-3dplot and pgfplots. It is not clear what the "best" convention is. However, translating between these conventions is a pain.