0

I am trying to generate a really large matrix but for some reason, I get an error when I try to compile it, Can someone help me to figure out why?

\documentclass[10pt,letterpaper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{lscape}
\begin{document}
\begin{landscape}
\begin{equation}
  \resizebox{1.65\textwidth}{!}{
    $\boldsymbol{\hat{\mathrm{H}}_{QQ}}=
    \begin{bmatrix}
      (\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})    
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})%   
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
%
(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}}) 
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}}) 
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})  
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})  
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\end{bmatrix}$}
\end{equation}
\end{landscape}
\end{document}
Mico
  • 506,678
  • 2
    You need to increase the maximum number of columns, e.g. by saying \setcounter{MaxMatrixCols}{20}, see this answer. –  Jun 14 '18 at 05:07
  • Please don't write \boldsymbol{\mathrm{...}}. (Your matrix features 242 [!!] instances of this atrocity.) Instead, please write \mathbf{...}. Your code will instantaneously become a lot more readable. – Mico Jun 14 '18 at 06:19
  • @marmot - Recommending \setcounter{MaxMatrixCols}{20} -- or \addtocounter{MaxMatrixCols}{1} -- would provide the OP with a bit more information about the nature of the problem and about how it can be fixed. – Mico Jun 14 '18 at 06:28
  • @Mico Well, I provided a link to an answer where there is some explanation. –  Jun 14 '18 at 11:50

1 Answers1

0

The problem was solved after adding the extra line suggested by the user marmot, \setcounter{MaxMatrixCols}{20}.

\documentclass[10pt,letterpaper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{lscape}
\begin{document}
\setcounter{MaxMatrixCols}{20}
\begin{landscape}
\begin{equation}
  \resizebox{1.65\textwidth}{!}{
    $\boldsymbol{\hat{\mathrm{H}}_{QQ}}=
    \begin{bmatrix}
      (\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})    
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})%   
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})%
&(\boldsymbol{\mathrm{Q^{I}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
%
(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}}) 
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{V}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}}) 
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})  
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VI}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})  
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})%
&(\boldsymbol{\mathrm{Q^{VII}_{3}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{I}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{II}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{III}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\\
(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{V}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VI}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{VII}_{3}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{I}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{II}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{III}_{5}}})
&(\boldsymbol{\mathrm{Q^{IV}_{5}}}\vert\hat{\mathrm{H}}\boldsymbol{\mathrm{Q^{IV}_{5}}})
\end{bmatrix}$}
\end{equation}
\end{landscape}
\end{document}