[Tex/LaTex] Matrix with lines and labels with arrows

Question

I am trying to reproduce something like this:

So far, I have got the matrix with the lines from the following code:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mleftright}

\begin{document}
\[
\renewcommand\arraystretch{1.3}
A_{ij} = \mleft[
\begin{array}{c|c|c|c|c}
     A_{c,\rho} & A_{c,u_r} & A_{c,u_{\theta}} & A_{c,u_z} & A_{c,T}     \\ \hline
     A_{r,\rho} & A_{r,u_r} & A_{r,u_{\theta}} & A_{r,u_z} & A_{r,T}    \\ \hline
     A_{\theta,\rho} & A_{\theta,u_r} & A_{\theta,u_{\theta}} & A_{\theta,u_z} & A_{u_{\theta},T}   \\ \hline
     A_{z,\rho} & A_{z,u_r} & A_{z,u_{\theta}} & A_{z,u_z} & A_{z,T}   \\ \hline
     A_{e,\rho} & A_{e,u_r} & A_{e,u_{\theta}} & A_{e,u_z} & A_{e,T}   
\end{array}
\mright]
\]

\end{document}

Now, how do I add the labels to rows and columns with arrows?

Answer 1

You can do it with blkarray. A couple of dummy columns are necessary for accommodating the horizontal rules.

\documentclass{article}
\usepackage{amsmath}
\usepackage{blkarray}

\begin{document}
\[
\renewcommand\arraystretch{1.3}
\begin{blockarray}{rcccccccc}
&&& u & v & w & \rho & T & \\
&&& \downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \\
\begin{block}{rc[c@{}c|c|c|c|c@{}c]}
\text{Cont.}  & \to && A_{c,u} & A_{c,v} & A_{c,w} & A_{c,\rho} & A_{c,T} &\vphantom{\smash[b]{\bigg|}} \\
\BAhhline{~~~-----~}
x\text{-mom}  & \to && A_{r,\rho} & A_{r,u_r} & A_{r,u_{\theta}} & A_{r,u_z} & A_{r,T} & \\
\BAhhline{~~~-----~}
A_{ij}=\quad
y\text{-mom}  & \to && A_{\theta,\rho} & A_{\theta,u_r} & A_{\theta,u_{\theta}} & A_{\theta,u_z} & A_{u_{\theta},T} & \\
\BAhhline{~~~-----~}
z\text{-mom}  & \to && A_{z,\rho} & A_{z,u_r} & A_{z,u_{\theta}} & A_{z,u_z} & A_{z,T} & \\
\BAhhline{~~~-----~}
\text{energy} & \to && A_{e,\rho} & A_{e,u_r} & A_{e,u_{\theta}} & A_{e,u_z} & A_{e,T} & \vphantom{\smash[t]{\bigg|}}\\
\end{block}
\end{blockarray}
\]

\end{document}

The \vphantom trick is for getting slightly bigger brackets.