how to make a matrix small

Question

how I can make this matrix small?

\[ 
G=\dfrac{1}{k(c_{k}^{2}+...+c^{2}_{n-1})+1} \begin{bmatrix}
2(c_{k}^{2}+...+c^{2}_{n-1})+1 & -c_{k}^{2}-...-c^{2}_{n-1}& -c_{k}^{2}-...-c^{2}_{n-1}&... & -c_{k}^{2}-...-c^{2}_{n-1}& c_{k}&c_{k+1}&...&c_{n-1}\\
-c_{k}^{2}-...-c^{2}_{n-1}& 2(c_{k}^{2}+...+c^{2}_{n-1})+1&...  & -c_{k}^{2}-...-c^{2}_{n-1}&c_{k}&c_{k+1}&...&c_{n-1}\\
\vdots &\vdots &\vdots & \vdots & \vdots\\
-c_{k}^{2}-...-c^{2}_{n-1}}& -c_{k}^{2}-...-c^{2}_{n-1}&...&2(c_{k}^{2}+...+c^{2}_{n-1})+1  & c_{k}&c_{k+1}&...&c_{n-1}\\
\end{bmatrix}
\]

Answer 1

I propose introducing a shortcut for the repeating expression, with an \intertext explaining the notation:

\documentclass{article}
\usepackage{ mathtools, nccmath}

\begin{document}

\begin{fleqn}
    \begin{align*}
    G =\mathrlap{\dfrac{1}{k(c_{k}^{2}+ \dots +c^{2}_{n-1})+1} \times{}} \\[1ex]
     &\times \begin{bmatrix}
    2A_{k}+1 & -A_{k} & -A_{k} & \dots & -A_{k} & c_{k} & c_{k+1}& \dots & c_{n-1}\\
    -A_{k} & 2A_{k} +1 & \dots & -A_{k} & c_{k} & c_{k+1} & \dots & c_{n-1}\\
    \vdots & \vdots & \vdots & \vdots & \vdots\\
    -A_{k} & -A_{k} & \dots & 2A_{k} + 1 & c_{k} & c_{k+1} & \dots &c_{n-1}
    \end{bmatrix}, \\
    \intertext[0.5ex]{where $\;A_{k} = c_{k}^{2}+ \dots +c^{2}_{n-1}$ }
    \end{align*}
\end{fleqn}

\end{document} 

Answer 2

Another rudimental answer using matrix and smallmatrix with mathtools package.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\begin{document}

\[
\begin{matrix}
G=\dfrac{1}{k(c_{k}^{2}+\ldots+c^{2}_{n-1})+1} \times & \\[1em]
\begin{bsmallmatrix}
2(c_{k}^{2}+\ldots+c^{2}_{n-1})+1 & -c_{k}^{2}-\ldots-c^{2}_{n-1}& -c_{k}^{2}-\ldots-c^{2}_{n-1}&\ldots& -c_{k}^{2}-\ldots-c^{2}_{n-1}& c_{k}&c_{k+1}&\ldots&c_{n-1}\\
-c_{k}^{2}-\ldots-c^{2}_{n-1}& 2(c_{k}^{2}+\ldots+c^{2}_{n-1})+1&\ldots& -c_{k}^{2}-\ldots-c^{2}_{n-1}&c_{k} & c_{k+1} & \ldots &c_{n-1}\\
\vdots &\vdots &\vdots & \vdots & \vdots\\
-c_{k}^{2}-\ldots-c^{2}_{n-1} & -c_{k}^{2}-\ldots-c^{2}_{n-1}&\ldots& 2(c_{k}^{2}+\ldots+c^{2}_{n-1})+1  & c_{k} & c_{k+1}& \ldots &c_{n-1}
\end{bsmallmatrix}
\end{matrix}
\]

\end{document}

Answer 3

You can use {bNiceMatrix} of nicematrix with the option small.

\documentclass[a4paper,12pt]{article}
\usepackage{nicematrix,amssymb}
\begin{document}

\[
\begin{matrix}
G=\dfrac{1}{k(c_{k}^{2}+\ldots+c^{2}_{n-1})+1} \times & \\[1em]
\begin{bNiceMatrix}[small]
2(c_{k}^{2}+\ldots+c^{2}_{n-1})+1 & -c_{k}^{2}-\ldots-c^{2}_{n-1}& -c_{k}^{2}-\ldots-c^{2}_{n-1}&\ldots& -c_{k}^{2}-\ldots-c^{2}_{n-1}& c_{k}&c_{k+1}&\ldots&c_{n-1}\\
-c_{k}^{2}-\ldots-c^{2}_{n-1}& 2(c_{k}^{2}+\ldots+c^{2}_{n-1})+1&\ldots& -c_{k}^{2}-\ldots-c^{2}_{n-1}&c_{k} & c_{k+1} & \ldots &c_{n-1}\\
\vdots &\vdots &\vdots & \vdots & \vdots\\
-c_{k}^{2}-\ldots-c^{2}_{n-1} & -c_{k}^{2}-\ldots-c^{2}_{n-1}&\ldots& 2(c_{k}^{2}+\ldots+c^{2}_{n-1})+1  & c_{k} & c_{k+1}& \ldots &c_{n-1}
\end{bNiceMatrix}
\end{matrix}
\]

\end{document}