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}