Equation number for each row of a matrix equation
Hmm! not really supported LaTeX syntax but
\documentclass{article}
\usepackage{amsmath}
\newsavebox\labelbox
\begin{document}
\savebox\labelbox{$\begin{matrix}
\refstepcounter{equation}(\theequation)\label{aa}\\
\refstepcounter{equation}(\theequation)\label{bb}\\
\refstepcounter{equation}(\theequation)\label{cc}
\end{matrix}$}
\[
\begin{bmatrix}
H & J^T & -Z^{\frac12} \\
J & -\delta I & \\
-Z^{\frac12} & & -X
\end{bmatrix}
\begin{bmatrix}
r \\ s \\ t
\end{bmatrix}
=
\lambda
\begin{bmatrix}
H & & \\
& U & \\
& & W
\end{bmatrix}
\begin{bmatrix}
r \\ s \\ t
\end{bmatrix}
\eqno
\usebox{\labelbox}
\]
[\ref{aa}]
[\ref{bb}]
[\ref{cc}]
\end{document}