Coloring the backgrounds of portions of a matrix

Question

I've been looking around for some time and I seem to be having a large bit of trouble coloring the following matrix:

\begin{pmatrix}  3 & -1 & -1 & -1 & 0 & 0 & 0 \\
        -1 & 1 & 0 & 0 & 0 & 0 & 0 \\
        -1 & 0 & 2 & 0 & 0 & 0 & 0 \\
        -1 & 0 & 0 & 2 & -1 & 0 & 0 \\
        0 & 0 & -1 & 0 & 3 & -1 & -1 \\
        0 & 0 & 0 & -1 & -1 & 3 & -1 \\
        0 & 0 & 0 & 0 & -1 & -1 & 2 \end{pmatrix}

As below:

Would anyone know where I would start to do this? Everything I've seem to come across seems to have been specially written for a particular matrix and I've been having trouble adapting the codes.

Answer 1

Apart from the possibilities listed in Zarko's comment, you can use tikzmark, which gives you an arguably finer automatic control. In your use-case, however, the finer control is not needed but it might be if you have more fancy entries in the matrix like stuff with exponents.

\documentclass{article}
\usepackage{eso-pic}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{tikzmark,fit}
\begin{document}
\AddToShipoutPictureBG{%
\begin{tikzpicture}[overlay,remember picture]
 \node[fill=blue!40,rounded corners,fit=(m1)(m3)]{};
 \node[fill=red!40,rounded corners,fit=(m2)(m4)]{};
 \node[fill=purple!60,inner xsep=1.6ex,rounded corners,fit=(m2)(m3)]{};
\end{tikzpicture}
}
\[\begin{pmatrix}  
    \tikzmarknode{m1}{3} & -1 & -1 & -1 & 0 & 0 & 0 \\
        -1 & 1 & 0 & 0 & 0 & 0 & 0 \\
        -1 & 0 & \tikzmarknode{m2}{2} & 0 & 0 & 0 & 0 \\
        -1 & 0 & 0 & \tikzmarknode{m3}{2} & -1 & 0 & 0 \\
        0 & 0 & -1 & 0 & 3 & -1 & -1 \\
        0 & 0 & 0 & -1 & -1 & 3 & -1 \\
        0 & 0 & 0 & 0 & -1 & -1 & \tikzmarknode{m4}{2}
\end{pmatrix}\]
\end{document}

---

Appendix (by BlackMild): This is a minor change from mamot's code. I remove the third node, and use opacity=.3 and inner sep=4pt for the first and the second nodes, so their colors are self-mixing.

\documentclass{article}
\usepackage{eso-pic}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{tikzmark,fit}
\begin{document}
\AddToShipoutPictureBG{%
\begin{tikzpicture}[overlay,remember picture,opacity=.3,inner sep=4pt]
\node[fill=blue,fit=(m1)(m3)]{};
\node[fill=red,fit=(m2)(m4)]{};
\end{tikzpicture}
}
    \[\begin{pmatrix}  
        \tikzmarknode{m1}{3} & -1 & -1 & -1 & 0 & 0 & 0 \\
        -1 & 1 & 0 & 0 & 0 & 0 & 0 \\
        -1 & 0 & \tikzmarknode{m2}{2} & 0 & 0 & 0 & 0 \\
        -1 & 0 & 0 & \tikzmarknode{m3}{2} & -1 & 0 & 0 \\
        0 & 0 & -1 & 0 & 3 & -1 & -1 \\
        0 & 0 & 0 & -1 & -1 & 3 & -1 \\
        0 & 0 & 0 & 0 & -1 & -1 & \tikzmarknode{m4}{2}
    \end{pmatrix}\]
\end{document}

Answer 2

You can easily do that with {pNiceMatrix} of nicematrix.

In that environment, you have a built-in command \Block and you can fill a block with the color you want.

In order to show that this works even in presence of a background, I have put the environment {pNiceMatrix} in a {tcolorbox} (user121799's answer does not work with a background).

\documentclass{article}
\usepackage{tcolorbox}
\usepackage{nicematrix,tikz}
\begin{document}
\begin{tcolorbox}
[\begin{pNiceMatrix}[margin]

\Block[fill=blue!40,rounded-corners]{4-4}{}
3  & -1 & -1 & -1 & 0  & 0  & 0  \
-1 & 1  & 0  & 0  & 0  & 0  & 0  \
-1 & 0  & \Block[fill=red!40,rounded-corners]{-}{}
          2  & 0  & 0  & 0  & 0  \
-1 & 0  & 0  & 2  & -1 & 0  & 0  \
0  & 0  & -1 & 0  & 3  & -1 & -1 \
0  & 0  & 0  & -1 & -1 & 3  & -1 \
0  & 0  & 0  & 0  & -1 & -1 & 2 
\end{pNiceMatrix}]
\end{tcolorbox}
\end{document}

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

You can use the key opacity (requires v. 6.22 of nicematrix).

\documentclass{article}
\usepackage{tcolorbox}
\usepackage{nicematrix}
\begin{document}
\begin{tcolorbox}
[\begin{pNiceMatrix}[margin]

\Block[fill=blue!40,rounded-corners]{4-4}{}
3  & -1 & -1 & -1 & 0  & 0  & 0  \
-1 & 1  & 0  & 0  & 0  & 0  & 0  \
-1 & 0  & \Block[fill=red!80,opacity=0.5,rounded-corners]{-}{}
          2  & 0  & 0  & 0  & 0  \
-1 & 0  & 0  & 2  & -1 & 0  & 0  \
0  & 0  & -1 & 0  & 3  & -1 & -1 \
0  & 0  & 0  & -1 & -1 & 3  & -1 \
0  & 0  & 0  & 0  & -1 & -1 & 2 
\end{pNiceMatrix}]
\end{tcolorbox}
\end{document}

If you want the red block behind the blue one, this technic won't work. In that case, it's possible to use the \CodeBefore provided by {pNiceMatrix} in order to draw the colored rectangles with Tikz before the construction of the array (using Tikz nodes created by nicematrix in the matrix).

Once again, this works even with a background.

\documentclass{article}
\usepackage{tcolorbox}
\usepackage{nicematrix,tikz}
\begin{document}
\begin{tcolorbox}
[\begin{pNiceMatrix}[margin]

\CodeBefore
  \begin{tikzpicture}
  \fill [red!40,rounded corners] (3-|3) rectangle (8-|8) ;
  \fill [blue!40,rounded corners] (1-|1) rectangle (5-|5) ;
  \end{tikzpicture}
\Body
3  & -1 & -1 & -1 & 0  & 0  & 0  \
-1 & 1  & 0  & 0  & 0  & 0  & 0  \
-1 & 0  & 2  & 0  & 0  & 0  & 0  \
-1 & 0  & 0  & 2  & -1 & 0  & 0  \
0  & 0  & -1 & 0  & 3  & -1 & -1 \
0  & 0  & 0  & -1 & -1 & 3  & -1 \
0  & 0  & 0  & 0  & -1 & -1 & 2 
\end{pNiceMatrix}]
\end{tcolorbox}
\end{document}