I want to do something like this:

But I don't find the way to align the matrix.
\documentclass[10pt]{article}
\usepackage[spanish]{babel}
\usepackage{amsmath, amssymb, amsthm, tikz}
\usepackage[margin=1in]{geometry}
\usetikzlibrary{babel}
\begin{document}
$$\begin{aligned}
\begin{matrix}
_{B}( T)_{A} & =([ coord_{B} T( v_{1})] ,\ [ coord_{b} T( v_{2})] ,\dotsc ,[ coord_{B}] T( v_{n})) \\
& =\begin{pmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{pmatrix}
\end{matrix}
\end{aligned}$$
\end{document}

