how to add caption above and alongside on Matrix

Question

can you help me with printing Matrix like picture below? I have no idea how to add the text above and alongside to Matrix in that way, and how to add those ellipses somewhere especially for sparse matrix? much appreciated.

Answer 1

The following example based on the kbordermatrix package might serve as a point to start from:

\documentclass{article}
\usepackage{amsmath}
\usepackage{kbordermatrix}
\begin{document}
[
  \kbordermatrix{
          & (2,2) & (2,3) & (2,4) \
    (2,2) & a_1   & a_2   & 0     & \cdots & 0 & a_3 & a_4 & 0 & \cdots & 0 & \cdots & 0\
    (2,3) & a_5   & 0     & a_6   & \cdots & 0 & a_7 & 0 & a_8 & \cdots & 0 & \cdots & 0  \
          & \
          &\
          &\
          &\vdots         &       & & & & \ddots & & & & & & \vdots \
          & \
          &\cdots         &       & & & & \cdots & & & & & & \cdots \
  }
]
\end{document}