¿Cómo rodear una sección de matriz en LaTeX?

Question

Actualmente estoy trabajando en un informe de laboratorio donde tengo que explicar el Método de Eliminación Gaussiana para una matriz. Como parte de mi explicación, quiero rodear porciones circulares/ovaladas de una matriz.

¿Hay alguna forma de rodear la diagonal principal de una matriz o una esquina de la misma? Fotos a continuación con ejemplos. Estoy pensando que quizás tenga que usar una \putestructura encima de un entorno de matriz/matriz, pero no sé cómo hacerlo.

EDITAR: Esto es lo que tengo actualmente para generar la matriz que dibujé en las imágenes:

\usepackage[utf8]{inputenc}
\usepackage{indentfirst}
\usepackage{graphicx}
\usepackage{setspace}
\usepackage[numbers]{natbib}
\usepackage [autostyle, english = american]{csquotes}
\MakeOuterQuote{"}
\usepackage{layout}
\usepackage[title]{appendix}
\usepackage[justification=centering]{caption}
\usepackage{titlesec}
\usepackage[percent]{overpic}
\usepackage{amsmath}
\usepackage{systeme}
\usepackage{blkarray, bigstrut}

...

\begin{center}
    \begin{blockarray}{cccc}
        \begin{block}{ [ ccc| c ]}
            \bigstrut[t]
             1 & -1 &  3 & -3 \\
            -1 &  0 & -2 &  1 \\
             2 &  2 &  4 &  0 \bigstrut[b] \\
        \end{block}
    \end{blockarray}
\end{center}

Answer 1

Aquí hay una posible forma de usar tikzmark.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{blkarray, bigstrut}
\usepackage{tikz}
\usetikzlibrary{tikzmark,calc,fit}
\begin{document}
\begin{center}
    \begin{blockarray}{cccc}
        \begin{block}{ [ ccc| c ]}
            \bigstrut[t]
             \tikzmarknode{A11}{1} & -1 &  3 & -3 \\
            -1 &  0 & -2 &  1 \\
             2 &  2 &  \tikzmarknode{A33}{4} &  0 \bigstrut[b] \\
        \end{block}
    \end{blockarray}
\end{center}
\begin{tikzpicture}[remember picture,overlay]
 \draw let \p1=($(A33)-(A11)$),\n1={atan2(\y1,\x1)} in 
 node[rotate fit=\n1,fit=(A11) (A33),draw,rounded corners,inner sep=2pt]{};
\end{tikzpicture}

\begin{center}
    \begin{blockarray}{cccc}
        \begin{block}{ [ ccc| c ]}
            \bigstrut[t]
             1 & -1 &  3 & -3 \\
            \tikzmarknode{B21}{-1} &  0 & -2 &  1 \\
             \tikzmarknode{B31}{2} &  \tikzmarknode{B32}{2} &  4 &  0 \bigstrut[b] \\
        \end{block}
    \end{blockarray}
\end{center}
\begin{tikzpicture}[remember picture,overlay]
\node[fit=(B21) (B31) (B32),inner sep=2pt] (FB){};
\path (FB.south east) arc(-90:45:4pt) coordinate(aux1);
\draw (aux1) arc(45:-90:4pt) -- ([xshift=4pt]FB.south west)
arc(-90:-180:4pt) -- (FB.north west) arc(180:45:4pt) -- cycle;
\end{tikzpicture}

\begin{center}
    \begin{blockarray}{cccc}
        \begin{block}{ [ ccc| c ]}
            \bigstrut[t]
             1 & \tikzmarknode{C12}{-1} &  \tikzmarknode{C13}{3} & -3 \\
             -1 &  0 & \tikzmarknode{C23}{-2} &  1 \\
             2 &  2 &  4 &  0 \bigstrut[b] \\
        \end{block}
    \end{blockarray}
\end{center}
\begin{tikzpicture}[remember picture,overlay]
\node[fit=(C12) (C23) (C13),inner sep=2pt] (FC){};
\path (FC.north west) arc(90:225:4pt) coordinate(aux2);
\draw (aux2) arc(225:90:4pt) -- ([xshift=-4pt]FC.north east)
arc(90:0:4pt) -- (FC.south east) arc(0:-135:4pt) -- cycle;
\end{tikzpicture}
\end{document}

Una solución más corta viene dada por

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{blkarray, bigstrut}
\usepackage{tikz}
\usetikzlibrary{tikzmark}
\begin{document}
\begin{center}
    \begin{blockarray}{cccc}
        \begin{block}{ [ ccc| c ]}
            \bigstrut[t]
             \tikzmarknode{A11}{1} & -1 &  3 & -3 \\
            -1 &  0 & -2 &  1 \\
             2 &  2 &  \tikzmarknode{A33}{4} &  0 \bigstrut[b] \\
        \end{block}
    \end{blockarray}
\end{center}
\begin{tikzpicture}[remember picture,overlay]
 \draw[red] plot[smooth cycle] coordinates {(A11.north)
 (A33.north east) (A33.south)  (A11.south west)};
\end{tikzpicture}

\begin{center}
    \begin{blockarray}{cccc}
        \begin{block}{ [ ccc| c ]}
            \bigstrut[t]
             1 & -1 &  3 & -3 \\
            \tikzmarknode{B21}{-1} &  0 & -2 &  1 \\
             \tikzmarknode{B31}{2} &  \tikzmarknode{B32}{2} &  4 &  0 \bigstrut[b] \\
        \end{block}
    \end{blockarray}
\end{center}
\begin{tikzpicture}[remember picture,overlay]
\draw[red] plot[smooth cycle] coordinates {(B21.north west) (B21.north east)
 (B32.north east) (B32.south east) (B31.south west)};
\end{tikzpicture}

\begin{center}
    \begin{blockarray}{cccc}
        \begin{block}{ [ ccc| c ]}
            \bigstrut[t]
             1 & \tikzmarknode{C12}{-1} &  \tikzmarknode{C13}{3} & -3 \\
             -1 &  0 & \tikzmarknode{C23}{-2} &  1 \\
             2 &  2 &  4 &  0 \bigstrut[b] \\
        \end{block}
    \end{blockarray}
\end{center}
\begin{tikzpicture}[remember picture,overlay]
\draw[red] plot[smooth cycle] coordinates {(C12.north west) (C13.north east)
 (C23.south east) (C23.south west) (C12.south west)};
\end{tikzpicture}
\end{document}

Si se reemplaza todo \tikzmarknodepor \tikzmarknode[inner sep=1pt], esto se convierte en