How can I get a fraction with a matrix in the numerator and denominator?

Question

The above fraction is what I would like to achieve

What I have so far is

$ \begin{bmatrix}
0 \\
0 \\
1 \\
1 
\end{bmatrix}   - \frac{ \begin{bmatrix}
0 & 0 & 1 & 1 
\end{bmatrix}  \begin{bmatrix}
1 \\
1 \\
1 \\
1 
\end{bmatrix}}{\begin{bmatrix}
1 & 1 & 1 & 1 
\end{bmatrix}  \begin{bmatrix}
1 \\
1 \\
1 \\
1 
\end{bmatrix} }$

and it looks like this

How can I achieve my desired result?

Answer 1

You could use the bsmallmatrix environment, provided by the mathtools package, to render the row and column vectors in the \frac expression more compactly.

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
\begin{bmatrix}
  0 \\ 0 \\ 1 \\ 1 
\end{bmatrix}   
- \frac{ 
\begin{bsmallmatrix}
  0 & 0 & 1 & 1 
\end{bsmallmatrix}  
\begin{bsmallmatrix}
  1 \\ 1 \\ 1 \\ 1 
\end{bsmallmatrix}}{%
\begin{bsmallmatrix}
  1 & 1 & 1 & 1 
\end{bsmallmatrix}  
\begin{bsmallmatrix}
  1 \\ 1 \\ 1 \\ 1 
\end{bsmallmatrix} }
\begin{bmatrix}
  1 \\ 1 \\ 1 \\ 1 
\end{bmatrix} 
\]
\end{document}

Answer 2

\documentclass{article}
\usepackage{tabstackengine}
\stackMath
\newcommand\Frac[2]{\frac{\addstackgap{#1}}{\addstackgap{#2}}}
\begin{document}
\[
  \setstacktabbedgap{1ex}
  \bracketVectorstack{0\\0\\1\\1} -
  \Frac{
    \bracketMatrixstack{0&0&1&1}\bracketVectorstack{1\\1\\1\\1}
  }{
    \bracketMatrixstack{1&1&1&1}\bracketVectorstack{1\\1\\1\\1}
  }
  \bracketVectorstack{1\\1\\1\\1}
\]
\end{document}

The smaller size of \Frac is also possible, with a small redefinition:

\documentclass{article}
\usepackage{tabstackengine}
\stackMath
\newcommand\Frac[2]{{%
  \setstackgap{L}{.7\normalbaselineskip}\TABstackMathstyle{\scriptstyle}%
  \frac{\addstackgap{#1}}{\addstackgap{#2}}%
}}
\begin{document}
\[
  \setstacktabbedgap{1ex}
  \bracketVectorstack{0\\0\\1\\1} -
  \Frac{
    \bracketMatrixstack{0&0&1&1}\bracketMatrixstack{1\\1\\1\\1}
  }{
    \bracketMatrixstack{1&1&1&1}\bracketMatrixstack{1\\1\\1\\1}
  }
  \bracketVectorstack{1\\1\\1\\1}
\]
\end{document}