braces spanning few rows or columns of a matrix in latex

Question

I am trying to put braces on matrix that cover just few rows or columns.

I have come kinda close for the columns but no idea for the rows.

This is the example I have been working on:

\documentclass{minimal}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
A = \begin{array}{c@{\!\!\!}l}
\left( \begin{array}[c]{ccc}
a1 & \cdots & aN\\
b1 & \cdots & bN\\
\vdots &  & \vdots\\
z1 & \cdots & zN \\

\end{array}  \right)

&
\begin{array}[c]{ll}
\left. \begin{array}{c} \vphantom{1cm}  \\ \vphantom{2*\vdots}
\\ \vphantom{1cm} \end{array} \right\} & \text{$n_1$ times} \\

\end{array}
\end{array}
\end{equation*}

\end{document}

which produces this:

Does anyone have any idea?

Answer 1

If you want to span only some rows, you can use nicematrix which will put a Tikz node behind each cell of the matrix and then use the commands of Tikz to draw the brace and its label.

\documentclass{minimal}
\usepackage{nicematrix,tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{equation*}
A = \begin{pNiceMatrix}%
a1 &\Hdotsfor{2} & aN\\
b1 &\Hdotsfor{2} & bN\\
\Vdots & & & \Vdots\\
z1 & \Cdots &\Cdots & zN \\
\CodeAfter
   \tikz
   \draw [decorate,decoration = brace]
        ([xshift=3mm]2-4.north east) to node [auto = left] {$n_1$ times} 
        ([xshift=3mm]4-4.south east) ;
\end{pNiceMatrix}
\end{equation*}
\end{document}

Answer 2

If you want to span all rows of a matrix, you have the rcases environment from mathtools (an extension of amsmath), which also simplifies the code for a matrix, with its pmatrix environment. I added some improvements, as I think the matrix looks nicer with 4 columns:

\documentclass{minimal}
\usepackage{mathtools}

\begin{document}

\begin{equation*}
\begin{rcases}\displaystyle
A = \begin{pmatrix}
a1 &\hdotsfor{2} & aN\\
b1 &\hdotsfor{2} & bN\\
\vdots & & & \vdots\\
z1 & \cdots &\cdots & zN \\
\end{pmatrix}
\end{rcases}
 \text{$n_1$ times}
\end{equation*}

\end{document}

Answer 3

You can construct a zero-width array next to your matrix containing elements that match the height of the matrix rows. This way you can place a \right\} where needed:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\[
  A = \begin{pmatrix}
      a_1  & \cdots &   a_N  \\
      b_1  & \cdots &   b_N  \\
    \vdots &        & \vdots \\
      z_1  & \cdots &   z_N  \\
  \end{pmatrix}
  \setlength{\arraycolsep}{0pt} % Avoid any column space in arrays that follow
  \begin{array}{ c }
    \vphantom{a_N} \\ % First row
    \left.\kern-\nulldelimiterspace
    \vphantom{\begin{array}{ c }
        b_N  \\ % Second row
      \vdots \\ % Third row
        z_N     % Fourth/last row
    \end{array}}
    \right\}\text{$n_1$ times}
  \end{array}
\]

\end{document}

Answer 4

This is the code that worked out for me.

\documentclass{minimal}
\usepackage{nicematrix}
\NiceMatrixOptions{transparent}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}

\begin{equation*}
A=\begin{pNiceMatrix}[name=matrix]
a1 &\hdotsfor{2} & aN\\
b1 &\hdotsfor{2} & bN\\
\vdots & & & \vdots\\
z1 & \cdots &\cdots & zN \\
\end{pNiceMatrix}
\tikz[remember picture,overlay]
\draw[decoration={brace},decorate,thick]  ([xshift=3mm]matrix-2-4.north east) -- node[right=6pt] {$n_1$ times} ([xshift=3mm]matrix-4-4.south east);
\end{equation*}

\end{document}

Answer 5

With version of nicematrix at least 5.16 (2021-06-20), it's also possible to provide a solution which does not use explicitely Tikz. The brace is a standard brace of LaTeX and not a brace of the Tikz library decorations.

\documentclass{minimal}
\usepackage{nicematrix}
\begin{document}
\begin{equation*}
A = 
\begin{NiceArray}{(ccc)@{\qquad}l}[nullify-dots]
    a1     & \Ldots        & aN     & \\
    b1     & \Ldots        & bN     & \\
    \Vdots & \hspace*{1cm} & \Vdots & n_1 \text{ times}\\
    z1     & \Cdots        & zN  \\
\CodeAfter
    \SubMatrix{.}{2-3}{4-3}{\rbrace}[xshift=3mm]
\end{NiceArray}
\end{equation*}
\end{document}

You need several compilations (because nicematrix uses PGF/Tikz nodes under the hood).