Place matrix and image side-by-side

Question

I am trying to place a matrix and an image side-by-side in a tabular format, using the following code (following the style in Image next to Equation).

\documentclass{article}
\usepackage{amsmath}
\usepackage[font=small]{caption}
\usepackage{graphicx}

\begin{document}

    \begin{figure}[h]
        \begin{tabular}{p{5cm}c}
            {\begin{equation*}
                H = 
                {\renewcommand{\arraystretch}{1.2}
                \begin{pmatrix}
                    0 & 1 & 0 & 1 & 0 & 0 & 1\\
                    1 & 1 & 1 & 0 & 1 & 0 & 0\\
                    0 & 0 & 1 & 0 & 1 & 1 & 1\\
                    1 & 0 & 0 & 1 & 0 & 1 & 0\\
                \end{pmatrix}}
            \end{equation*}}
            &
            \includegraphics[scale=0.8]{"Tanner Graph"}
        \end{tabular}
        \caption{(above) parity check matrix of an $[8, 4, 4]_2$ code, and (below) the corresponding Tanner graph. Technically, this example matrix is not low-density, as it is too small}
        \label{Figure 1}
    \end{figure}


\end{document}

However, where I expect to see the two objects side-by-side, instead I get the following:

What should be done to achieve the desired layout?

Answer 1

Two changes were needed. First, to remove the matrix from the equation* environment, and instead place it between $ delimiters, with \displaystyle added, if needed. This will keep the matrix symmetric about the math axis, without any line feeds and spaces interjected. Second, the image, which is otherwise sits on the baseline, had to be surrounded with $\vcenter{\hbox{...}}$ to get it centered on the math axis.

\documentclass{article}
\usepackage{amsmath}
\usepackage[font=small]{caption}
\usepackage[demo]{graphicx}

\begin{document}

    \begin{figure}[h]
        \begin{tabular}{p{5cm}c}
            {$\displaystyle
                H = 
                {\renewcommand{\arraystretch}{1.2}
                \begin{pmatrix}
                    0 & 1 & 0 & 1 & 0 & 0 & 1\\
                    1 & 1 & 1 & 0 & 1 & 0 & 0\\
                    0 & 0 & 1 & 0 & 1 & 1 & 1\\
                    1 & 0 & 0 & 1 & 0 & 1 & 0\\
                \end{pmatrix}}
            $}
            &
            $\vcenter{\hbox{\includegraphics[scale=0.8]{"Tanner Graph"}}}$
        \end{tabular}
        \caption{(above) parity check matrix of an $[8, 4, 4]_2$ code, and (below) the corresponding Tanner graph. Technically, this example matrix is not low-density, as it is too small}
        \label{Figure 1}
    \end{figure}


\end{document}