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  • Matrices with side curly brackets
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If you are looking for the following behaviour
Use the following latex code

\usepackage{amsmath}


\begin{equation*}
  \mathbf{X} = \begin{array}{c@{\!\!\!}l}
  \left[ \begin{array}[c]{ccccc}
    1 & 0 & 0 & \cdots & 0 \\
    \vdots & \vdots & \vdots && \vdots \\
    1 & 0 & 0 & \cdots & 0 \\
    \hline
    1 & 1 & 0 & \cdots & 0 \\
    \vdots & \vdots & \vdots && \vdots \\
    1 & 1 & 0 & \cdots & 0 \\
    \hline
    1 & 0 & 1 & \cdots & 0 \\
    \vdots & \vdots & \vdots && \vdots \\
    1 & 0 & 1 & \cdots & 0 \\
    \hline
    \vdots & \vdots & \vdots && \vdots \\
    \hline
    1 & 0 & 0 & \cdots & 1 \\
    \vdots & \vdots & \vdots && \vdots \\
    1 & 0 & 0 & \cdots & 1 \\
  \end{array}  \right]
&
 \begin{array}[c]{@{}l@{\,}l}
   \left. \begin{array}{c} \vphantom{0}  \\ \vphantom{\vdots}
   \\ \vphantom{0} \end{array} \right\} & \text{$n_1$ times} \\
\left. \begin{array}{c} \vphantom{0} \\ \vphantom{\vdots}
   \\ \vphantom{0}  \end{array} \right\} & \text{$n_2$ times} \\
\left. \begin{array}{c} \vphantom{0}
  \\ \vphantom{\vdots} \\ \vphantom{0} \end{array} \right\} & \text{$n_3$ times} \\
  \vphantom{\vdots} & \\ \left. \begin{array}{c} \vphantom{0}
  \\ \vphantom{\vdots} \\ \vphantom{0} \end{array} \right\} & \text{$n_l$ times}
\end{array}
\end{array}
\end{equation*}
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