jacobian.tex

\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage{amsthm}
\newcommand{\RR}{\mathbf{R}}

\begin{document}
We define diffeomorphism $\phi \colon \RR^2 \to \RR^2$ by identify:
\[
  \phi(x, y) = (x, y).
\]

Then jacobian of $\phi$ is identity matrix:
\begin{align*}
  J_\phi = \begin{pmatrix}
    1 && 0 \\
    0 && 1
  \end{pmatrix}.
\end{align*}

\end{document}