This code
\begin{bmatrix}
a_{11} & a_{12} & a_{13} & a_{14} \\
a_{21} & a_{22} & a_{23} & a_{24} \\
a_{31} & a_{32} & a_{33} & a_{34}
\end{bmatrix}
\begin{bmatrix}
5 & 6 & 7 & 8 \\
4 & 3 & 2 & 1 \\
6 & 7 & 8 & 9
\end{bmatrix}
generates two matrices side by side. How can I make them on top of each other?
I suggest you place both bmatrix environments inside a gather* environment.
\documentclass{article}
\usepackage{amsmath} % for 'bmatrix' and 'gather*' environments
\begin{document}
\begin{gather}
\begin{bmatrix}
a_{11} & a_{12} & a_{13} & a_{14} \
a_{21} & a_{22} & a_{23} & a_{24} \
a_{31} & a_{32} & a_{33} & a_{34}
\end{bmatrix} \ % <-- force a line break
\begin{bmatrix}
5 & 6 & 7 & 8 \
4 & 3 & 2 & 1 \
6 & 7 & 8 & 9
\end{bmatrix}
\end{gather}
\end{document}
Here are some options; in principle, wrap the two matrices inside an array and separate them using a regular line break \\:
\documentclass{article}
\usepackage{amsmath,eqparbox}
% https://tex.stackexchange.com/a/34412/5764
\makeatletter
\NewDocumentCommand{\eqmathbox}{o O{c} m}{%
\IfValueTF{#1}
{\def\eqmathbox@##1##2{\eqmakebox[#1][#2]{$##1##2$}}}
{\def\eqmathbox@##1##2{\eqmakebox{$##1##2$}}}
\mathpalette\eqmathbox@{#3}
}
\makeatother
\begin{document}
[
\begin{bmatrix}
a_{11} & a_{12} & a_{13} & a_{14} \
a_{21} & a_{22} & a_{23} & a_{24} \
a_{31} & a_{32} & a_{33} & a_{34}
\end{bmatrix}
\begin{bmatrix}
5 & 6 & 7 & 8 \
4 & 3 & 2 & 1 \
6 & 7 & 8 & 9
\end{bmatrix}
]
[
\begin{array}{@{} c @{}}
\begin{bmatrix}
a_{11} & a_{12} & a_{13} & a_{14} \
a_{21} & a_{22} & a_{23} & a_{24} \
a_{31} & a_{32} & a_{33} & a_{34}
\end{bmatrix} \
\begin{bmatrix}
5 & 6 & 7 & 8 \
4 & 3 & 2 & 1 \
6 & 7 & 8 & 9
\end{bmatrix}
\end{array} \qquad
\begin{array}{@{} c @{}}
\begin{bmatrix}
\eqmathbox[aa]{a_{11}} & \eqmathbox[aa]{a_{12}} & \eqmathbox[aa]{a_{13}} & \eqmathbox[aa]{a_{14}} \
a_{21} & a_{22} & a_{23} & a_{24} \
a_{31} & a_{32} & a_{33} & a_{34}
\end{bmatrix} \
\[\dimexpr-\normalbaselineskip+\jot]
\begin{bmatrix}
\eqmathbox[aa]{5} & \eqmathbox[aa]{6} & \eqmathbox[aa]{7} & \eqmathbox[aa]{8} \
4 & 3 & 2 & 1 \
6 & 7 & 8 & 9
\end{bmatrix}
\end{array}
]
\end{document}
The addition of eqparbox (and \eqmathbox) depends on whether you want the entries to be aligned across the bmatrix-es. You can also consider blkarray.
Maybe the OP wants the columns of the first matrix aligned with the columns of the second. It's possible with {NiceMatrix} of nicematrix.
\documentclass{article}
\usepackage{nicematrix}
\begin{document}
[\begin{NiceMatrix}
a_{11} & a_{12} & a_{13} & a_{14} \
a_{21} & a_{22} & a_{23} & a_{24} \
a_{31} & a_{32} & a_{33} & a_{34} \[1mm]
5 & 6 & 7 & 8 \
4 & 3 & 2 & 1 \
6 & 7 & 8 & 9
\CodeAfter
\SubMatrix[{1-1}{3-4}]
\SubMatrix[{4-1}{6-4}]
\end{NiceMatrix}]
\end{document}
You need several compilations (because nicematrix uses PGF/Tikz nodes under the hood).
\documentclass{article} \usepackage{amsmath,stackengine} \stackMath \begin{document} \[ \stackon{ \begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\ a_{21} & a_{22} & a_{23} & a_{24} \\ a_{31} & a_{32} & a_{33} & a_{34} \end{bmatrix} }{ \begin{bmatrix} 5 & 6 & 7 & 8 \\ 4 & 3 & 2 & 1 \\ 6 & 7 & 8 & 9 \end{bmatrix} } \] \end{document}– Steven B. Segletes Aug 23 '21 at 18:12\documentclass{article} \usepackage{amsmath} \begin{document} \[ \begin{matrix} {\begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\ a_{21} & a_{22} & a_{23} & a_{24} \\ a_{31} & a_{32} & a_{33} & a_{34} \end{bmatrix}}\\ {\begin{bmatrix} 5 & 6 & 7 & 8 \\ 4 & 3 & 2 & 1 \\ 6 & 7 & 8 & 9 \end{bmatrix}} \end{matrix} \] \end{document}...but only if columns need not align – Steven B. Segletes Aug 23 '21 at 18:17