How to place arrows horizontally and vertically beside matrix?

Question

I would like to create a matrix with arrows next to it. Say, I created a 10x10 matrix in Latex. Then, I want to put one arrow parallel to the "x-axis" of the matrix and I want to label the arrow, e.g. with "variables". The same for the vertical axis which I want to label, say, "observations".

Is there any way to do this in Latex? Thanks in advance!

Answer 1

Try this. Both arrows should automatically expand base on the size of the matrix. You may want to shorten the horizontal arrow a bit, but it'd be hard to do without manually specifying the width of the matrix through the use of custom spacer such as \hphantom{\hrule{1cm}} replacing the \hphantom part of the code below, unless someone has better idea.

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\newcommand{\mymatrix}[1]{\ensuremath{\left\downarrow\vphantom{#1}\right.\overset{\xrightarrow[\hphantom{#1}]{\text{variables}}}{#1}}}
\begin{equation*}
\text{\tiny observations}\mymatrix{\begin{pmatrix}
        a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\
        a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\
        \vdots  & \vdots  & \ddots & \vdots  \\
        a_{m,1} & a_{m,2} & \cdots & a_{m,n}
        \end{pmatrix}}
\end{equation*}
\end{document}