Block matrix with partial vertical line

Question

I would like to create a partial block matrix, with two blocks on the bottom row, separated by a vertical line between them, and separated from the rest of the matrix by a horizontal line.

My first attempt captured the idea, but the alignment was lacking

\documentclass{article}

\usepackage{amsmath}

\newcommand{\bigzero}{\mbox{\normalfont\Large\bfseries 0}}
\newcommand{\bigid}{\mbox{\normalfont\Large\bfseries I}}

\begin{document}
  \begin{equation*}
    \begin{pmatrix}
      \begin{matrix}
        1 & x_0 & x_0^2  & \dots & x_0^n \\
          &     & \vdots &       & \\
        1 & x_m & x_m^2  & \dots & x_m^n \\
      \end{matrix} \\
      \hline
      \begin{array}{c c | c c c}
        \bigzero & & & \bigid_{n-m} &
      \end{array}
    \end{pmatrix}
  \end{equation*}
\end{document}

Ideally, I would like a little more space between the horizontal line and the rows. Furthermore, the 0 should be centred between the first two columns, while the I should be centred between the last three columns.

I was able to obtain a much better spacing using the nicematrix package, however I have no idea how to produce the vertical line, which should join with the horizontal line but not spread into the first three rows.

\documentclass{article}

\usepackage{amsmath}
\usepackage{nicematrix}

\newcommand{\bigzero}{\mbox{\normalfont\Large\bfseries 0}}
\newcommand{\bigid}{\mbox{\normalfont\Large\bfseries I}}

\begin{document}
  \begin{equation*}
    \begin{pNiceArray}{CCCCC}
      1 & x_0 & x_0^2  & \cdots & x_0^n \\
        &     & \Vdots &       & \\
      1 & x_m & x_m^2  & \cdots & x_m^n \\
      \hline
      \Block{2-2}{\bigzero} & & \Block{2-3}{\bigid_{n-m}} &  \\
      & & & &
    \end{pNiceArray}
  \end{equation*}
\end{document}

Answer 1

You can draw the rule you want with a TikZ instruction:

\documentclass{article}

\usepackage{nicematrix}
\usepackage{tikz}

\newcommand{\bigzero}{\mbox{\normalfont\Large\bfseries 0}}
\newcommand{\bigid}{\mbox{\normalfont\Large\bfseries I}}

\begin{document}
  \begin{equation*}
    \begin{pNiceMatrix}
      1 & x_0 & x_0^2  & \Cdots & x_0^n \\
        &     & \Vdots &       & \\
      1 & x_m & x_m^2  & \Cdots & x_m^n \\
      \hline
      \Block{2-2}{\bigzero} & & \Block{2-3}{\bigid_{n-m}} &  \\
      & & & &
      \CodeAfter
      \tikz \draw (4-|3) -- (6-|3) ;
    \end{pNiceMatrix}
  \end{equation*}
\end{document}

---

With recent versions of nicematrix, you can merely use the key borders of the command \Block:

\documentclass{article}
\usepackage{nicematrix}

\newcommand{\bigzero}{\mbox{\normalfont\Large\bfseries 0}}
\newcommand{\bigid}{\mbox{\normalfont\Large\bfseries I}}

\begin{document}
  \begin{equation*}
    \begin{pNiceArray}{ccccc}
      1 & x_0 & x_0^2  & \cdots & x_0^n \\
        &     & \Vdots &       & \\
      1 & x_m & x_m^2  & \cdots & x_m^n \\
      \Hline
      \Block[borders=right]{2-2}{\bigzero} & & \Block{2-3}{\bigid_{n-m}} &  \\
      & & & &
    \end{pNiceArray}
  \end{equation*}
\end{document}

Answer 2

You can also use two instructions \multicolumn:

\documentclass{article}

\usepackage{amsmath}
\usepackage{nicematrix}

\newcommand{\bigzero}{\mbox{\normalfont\Large\bfseries 0}}
\newcommand{\bigid}{\mbox{\normalfont\Large\bfseries I}}

\begin{document}
  \begin{equation*}
    \begin{pNiceMatrix}
      1 & x_0 & x_0^2  & \Cdots & x_0^n \\
        &     & \Vdots &       & \\
      1 & x_m & x_m^2  & \Cdots & x_m^n \\
      \hline
      \Block{2-2}{\bigzero} & \multicolumn{1}{C|}{} & \Block{2-3}{\bigid_{n-m}} &  \\
      & \multicolumn{1}{C|}{} & & &
    \end{pNiceMatrix}
  \end{equation*}
\end{document}