Here's a solution that steals from one of the answers to Passing parameters to a document
The command pdflatex wrapper myequation produces a pdf with just

with this wrapper.tex
\def\ReadCommandLineArg#1 {%
\def\CommandLineArg{#1}%
\input{\jobname}}
\unless\ifdefined\CommandLineArg
\endinput\expandafter\expandafter\expandafter\ReadCommandLineArg\fi
\documentclass{article}
\pagestyle{empty} % suppress page number
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\input{\CommandLineArg}
\end{equation*}
\end{document}
and your myequation.tex
A_{m,n} =
\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}
If there's more white space than you want in the pdf you can crop it with pdfcrop.
I don't know what you mean by "set the font size". You could probably tinker with this idea to make it do that.
Edit: to crop automatically, use the standalone package with $...$ instead of the equation* environment, as in the other answer.
\def\ReadCommandLineArg#1 {%
\def\CommandLineArg{#1}%
\input{\jobname}}
\unless\ifdefined\CommandLineArg
\endinput\expandafter\expandafter\expandafter\ReadCommandLineArg\fi
\documentclass{standalone}
\usepackage{amsmath}
\begin{document}
$\input{\CommandLineArg}$
\end{document}
And, answering a question you haven't asked, but that may come up, you can have multiple aligned equations if you use aligned and not align:
\begin{aligned}
e^{i\pi} & = \cos(\pi) + i\sin(\pi) \\
& = -1
\end{aligned}
\documentclass<...>and\begin<..>tags, that's exactly what I'm trying to avoid. I don't have documents, I have math equations written using the tex syntax . – user2485710 May 03 '14 at 23:15\usepackage{amsmath}(for thepmatrixenvironment), which would then require a\documentclass{<...>}(for the\usepackage{<...>}). – Paul Gessler May 03 '14 at 23:33+sign. – user2485710 May 03 '14 at 23:35