# horizontally align two minipages with matrizes

I'm trying to set two matrizes side by side, but I can't manage to horizontally align the matrizes. This is my example:

\documentclass[a4paper]{scrbook}
\usepackage{amsmath}
\begin{document}

\begin{minipage}[c][8.5cm]{0.48\textwidth}
\begin{align*}
\boldsymbol{\Lambda} &= \left(\begin{array}{c c c c}
1 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 \\
1 & 2 & 0 & 0 \\
1 & 3 & 0 & 0 \\
1 & 3 & 1 & 0 \\
1 & 3 & 2 & 0 \\
1 & 3 & 3 & 0 \\
1 & 3 & 4 & 0 \\
1 & 3 & 5 & 0 \\
1 & 3 & 6 & 0 \\
1 & 3 & 6 & 1 \\
1 & 3 & 6 & 2 \\
\end{array}\right)\\
\end{align*}
\end{minipage}
\begin{minipage}[c][8.5cm]{0.48\textwidth}
\begin{align*}
\boldsymbol{\eta} &= \left(\begin{array}{c}
\alpha_i\\
\beta_{1i}\\
\beta_{2i}\\
\beta_{3i}
\end{array}\right)
\end{align*}
\end{minipage}

\end{document}


Which results in:

So I would like the equal sign to be horizontally aligned. I've tried playing around with the height of the minipage, but that didn't work, and I'm not even sure, if using minipages to do this is the right approach for what I want.

No need to employ minipage environments, and no need for align* environments either. Do use pmatrix environments to typeset the two matrices, though.
\documentclass[a4paper]{scrbook}
$\boldsymbol{\Lambda} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 2 & 0 & 0 \\ 1 & 3 & 0 & 0 \\ 1 & 3 & 1 & 0 \\ 1 & 3 & 2 & 0 \\ 1 & 3 & 3 & 0 \\ 1 & 3 & 4 & 0 \\ 1 & 3 & 5 & 0 \\ 1 & 3 & 6 & 0 \\ 1 & 3 & 6 & 1 \\ 1 & 3 & 6 & 2 \end{pmatrix} \hspace{3cm} % set a suitable amount of horiz. spacing \boldsymbol{\eta} = \begin{pmatrix} \alpha_i\\ \beta_{1i}\\ \beta_{2i}\\ \beta_{3i} \end{pmatrix}$