# beamer two columns figure and formula

I am trying to do a beamer slide with two columns, one with an image and the other with a matrix more or less big. The code that I have is the following

\begin{frame}{Frame}
\frametitle{Minimal grid example}
\begin{columns}
\column{0.4\textwidth}
\includegraphics[scale=0.2]{image.pdf}
\column{0.4\textwidth}
$$\begin{pmatrix} 0 && 0 && 1 && 0 && 0 && 0 && 0 && 0 \\ 0 && 0 && 0 && 0 && 0 && 1 && 0 && 0 \\ t && -r^* && 0 && 0 && 0 && 0 && 0 && 0 \\ 0 && 0 && 0 && 0 && 0 && 0 && 0 && 1 \\ 0 && 0 && 0 && 0 && 0 && 0 && 1 && 0 \\ r && t* && 0 && 0 && 0 && 0 && 0 && 0 \\ 0 && 0 && 0 && 0 && 1 && 0 && 0 && 0 \\ 0 && 0 && 0 && 1 && 0 && 0 && 0 && 0 \end{pmatrix}.$$
\end{columns}
\end{frame}


but for some reason, the matrix is stretched to fill the whole right column. How can I manipulate the size of the formula?

\documentclass[demo]{beamer}
\usepackage{mathtools}

\begin{document}
\begin{frame}{Frame}
\frametitle{Minimal grid example}
\begin{columns}
\column{0.5\textwidth}
\centering
\includegraphics[width=\linewidth]{image.pdf}
\column{0.5\textwidth}
\setlength\arraycolsep{3pt}
$$\begin{pmatrix} 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ t & -r^* & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ r & t* & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \end{pmatrix}.$$
\end{columns}
\end{frame}
\end{document}


I made three changes:

• replace && with & (I don't understand of purpose of double ampersands, you only cross limit of normal matrix size -- 10 columns)
• reduce column separation in matrix
• change size of columns