Some matrices are not meant to be typeset.
You have specifically mentioned not to fiddle with the right part but I can't see any special treatment as white spaces are gobbled in the math mode and you have enabled it via matrix of math nodes
.
Anyway, here is an idea.
\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,tikz}
\usetikzlibrary{arrows,chains,matrix,positioning,scopes}
\begin{document}
We regret to state that we can not publish the following matrix in any journal in its current state. We
encourage the authors leave these all behind.
\begin{equation}
\begin{pmatrix}
\begin{tikzpicture}[every node/.style={minimum width=1.5em}]
\matrix (m1) [matrix of math nodes]
{
0 & 0 & A & A' \\
0 & 0 & B' & B \\
C & C' & 0 & 0 \\
D' & D & 0 & 0 \\
};
\matrix (m2) at (m1-4-4.south east) [anchor=m2-1-1.north west,
matrix of math nodes]
{
0 & 0 & K & K' \\
0 & 0 & L' & L \\
M & M' & 0 & 0 \\
N' & N & 0 & 0 \\
};
\node[scale=2] at (m1 |- m2) {$0$};
\node[scale=2,anchor=west] (kron) at ([xshift=-5mm]m2.east) {$\otimes T$};
\node[scale=2] at (m1 -| m2-1-4) {$0$};
\matrix (m3) at ([xshift=5pt]kron.east |- m1-1-4.north east)
[matrix of math nodes,anchor=m3-1-1.north west]
{
A' & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & B' & 0 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & C' & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & D' & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & E' & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & ASD' & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & H & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & 0 & G & I'0\\
};
\draw (m1-1-4.north east) -- (m1-1-4.north east |- m2-4-1.south west);
\draw (m1-1-4.north east -| m3.west) -- (m3.west |- m3-8-1.south east);
\draw (m1-4-1.south west) -- (m3-4-9.south east);
\end{tikzpicture}
\end{pmatrix}
\end{equation}
\end{document}

Actually there is a strong structure in your matrix though I don't know how to express it without typing it out completely. So here is an attempt to describe it. By making it 8x8 and removing all the dots because currently they are wrong. 1 ... 0
doesn't make any sense and also ambiguous. The superscripted c terms and others can be grouped and that makes the matrix a block partitioned one.
\documentclass{article}
\usepackage{amsmath}
\usepackage{rotating}
\begin{document}
\begin{sideways}
\thispagestyle{empty}%
\makebox[\textheight][c]{\begin{minipage}{\paperheight}
\setlength\arraycolsep{4pt}
\begin{align*}
&\left[ {\begin{array}{ccccccccccc}
1 & 0 & 0 &0 & -P(N_k^a|L_k^c) & 0 & 0 &0\\
-P(N_{k+1}^d|L_{k+1}^c) & 1 & 0 &0 & 0 & -P(N_{k+1}^a|L_{k+1}^c) & 0 &0\\
0 & -P(N_{k+2}^d|L_{k+2}^c) & 1 &0 & 0 & 0 &-P(N_{k+2}^a|L_{k+2}^c) &0\\
0 & 0 & -P(N_{c-1}^d|L_{c-1}^c) & 1 & 0 & 0 & 0 & -P(N_{c-1}^a|L_{c-1}^c)\\
-P(N_{k+1}^d|L_{k+1}) & 0 & 0 &0 & 1 & -P(N_{k+1}^a|L_{k+1}) & 0 &0\\
0 & -P(N_{k+2}^d|L_{k+2}) & 0 &0 & 0 & 1 &-P(N_{k+2}^a|L_{k+2}) &0\\
0 & 0 & -P(N_{c-1}^d|L_{c-1}) &0 & 0 & 0 & 1 &-P(N_{c-1}^a|L_{c-1})\\
0 & 0 & 0 & -P(N_c^d|L_c) & 0 & 0 & 0 & 1
\end{array} } \right]
\cdot\left[ {\begin{array}{c}
E(\widetilde{A}_{kk}^{cn}|L_k^c)\\
E(\widetilde{A}_{k k+1}^{cn}|L_{k+1}^c)\\
E(\widetilde{A}_{k k+2}^{cn}|L_{k+2}^c)\\
E(\widetilde{A}_{k c-1}^{cn}|L_{c-1}^c)\\
E(\widetilde{A}_{k k+1}^{cn}|L_{k+1})\\
E(\widetilde{A}_{k k+2}^{cn}|L_{k+2})\\
E(\widetilde{A}_{k c-1}^{cn}|L_{c-1})\\
E(\widetilde{A}_{kc}^{cn}|L_{c})\\
\end{array} } \right]\\
&= \begin{bmatrix}K &L\\M&N\end{bmatrix}\begin{bmatrix}E^c_1\\E_2\end{bmatrix}
\end{align*}
\end{minipage}}
\end{sideways}
\newpage
where
\begin{align*}
K_{mm} &= 1, \\
K_{m,m-1} &= -P(N_{k+m}^d|L_{k+m}^c),\\
N_{mm} &= 1, \\
N_{m-1,m} &= -P(N_{k+m}^a|L_{k+m}),\\
\end{align*}
and zero otherwise for $m=1,\ldots,c-(k+1)$. Similarly $L,M$ are diagonal matrices such that
\begin{align*}
L &=\operatorname{diag}\{-P(N_{k+m}^a|L_{k+m}^c)\}\\
M &=\operatorname{diag}\{-P(N_{k+m}^d|L_{k+m}) \}
\end{align*}
for $m=0,\ldots,c-(k+1)$.
\end{document}

So I would use K,L,M,N and put a description along the lines of

instead of fitting a beast in a journal paper. I need to warn you that this has the structure of a linear system Ax=b
and I didn't include the operation on b
in the document. But it is essentially a row permutation with 1,3,5,7,...2,4,6,....
Best Answer
You can have something very close to unlimited paper: Maximum papersize. The following example will output a pdf shrinked to the page size you need:
just change
MaxMatrixCols
to the value you need. result is (click on image for larger image):Old Method: I would select some papersize like A3 (or manually specify with
paperwidth=50in,paperheight=50in
as suggested)and than rescale the matrix. because pdf is a vector based file format, you can simply zoom in or print at bigger sheet of paper. I have a MWE with a 50x50 Matrix here:remember to set the
MaxMatrixCols
counter to your needs.