Coloured half lines in a matrix

Question

I was wondering how I could create this matrix in LaTeX:

I know how to do the matrix part but my question is the lines, how can I make them stop in (1,1), (2,2) and (3,3)?

Answer 1

Here is a possibility with nicematrix and tikz.

\documentclass{article}

\usepackage{nicematrix, tikz}

\begin{document}

\[
\NiceMatrixOptions{cell-space-limits = 2pt}
\begin{pNiceMatrix}[first-col]
\color{red}\Delta_1 & \frac{\partial^2f}{\partial x_1^2} & \frac{\partial^2f}{\partial x_1^2} & \frac{\partial^2f}{\partial x_1^2}\\
\color{green}\Delta_2 & \frac{\partial^2f}{\partial x_1^2} & \frac{\partial^2f}{\partial x_1^2} & \frac{\partial^2f}{\partial x_1^2}\\
\color{blue}\Delta_3 & \frac{\partial^2f}{\partial x_1^2} & \frac{\partial^2f}{\partial x_1^2} & \frac{\partial^2f}{\partial x_1^2}
\CodeAfter
\tikz{
    \draw[red, shorten >=-3mm] (1-|2) -- (2-|2) -- (2-|1);
    \draw[green, shorten >=-3mm] (1-|3) -- (3-|3) -- (3-|1);
    \draw[blue, shorten >=-3mm] (1-|4) -- (4-|4) -- (4-|1);
}
\end{pNiceMatrix}
\]

\end{document}