partitioned matrix

Question

Please tell me the way to code latex to produce a matrix whose form is in the following image. Many thanks. My current code is not the desired one.

    \documentclass[a4paper]{article}
    \usepackage{amsmath}
    \begin{document}
    \begin{equation}
    U^{(k+1)}_a=
    \left(
    \begin{array}{ccccc|c}
    &  &  &  &  & \left(U^{(k+1)}_a\right)_{0k} \\
    &  &  &  &  & \left(U^{(k+1)}_a\right)_{1k} \\
    &  &  U^{(k)}_a  &  &  & \vdots \\
    &  &  &  &  & \vdots \\
    &  &  &  &  & \vdots \\
    \hline
    a_k & 0 & \dots & 0 & 0 & \left (U^{(k+1)}_a\right)_{kk}
    \end{array}
    \right).
    \end{equation}
    \end{document}

Answer 1

This can be done using the \multicolumn command. The \cline command makes the partial horizontal line. The 1-column \multicolumn in the last row eliminates the last portion of the vertical line. Using \multicolumn for the U^{(k)}_a entry automatically centers it horizontally instead of placing it in the third column.

I also added a bit of space between your rows by setting \arraystretch to 1.6.

\documentclass[a4paper]{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
U^{(k+1)}_a=
\left(
\renewcommand{\arraystretch}{1.6}
\begin{array}{ccccc|c}
&  &  &  &  & \left(U^{(k+1)}_a\right)_{0k} \\
&  &  &  &  & \left(U^{(k+1)}_a\right)_{1k} \\
\multicolumn{5}{c|}{U^{(k)}_a} & \vdots \\
&  &  &  &  & \vdots \\
&  &  &  &  & \vdots \\
\cline{1-5}
a_k & 0 & \dots & 0 & \multicolumn{1}{c}{0} & \left (U^{(k+1)}_a\right)_{kk}
\end{array}
\right).
\end{equation}
\end{document}

I would also probably delete the 4th column and two of the rows of \vdots, and use \cdots instead of \dots, but that's just my opinion. If you add \usepackage{array} you'll get a cleaner join between the horizontal and vertical lines.

U^{(k+1)}_a=
\left(
\renewcommand{\arraystretch}{2}
\begin{array}{cccc|c}
&  &  &  & \left(U^{(k+1)}_a\right)_{0k} \\
    \multicolumn{4}{c|}{U^{(k)}_a} & \left(U^{(k+1)}_a\right)_{1k} \\
&  &  &  & \vdots \\
\cline{1-4}
a_k & 0 & \cdots & \multicolumn{1}{c}{0} & \left (U^{(k+1)}_a\right)_{kk}
\end{array}
\right).

Answer 2

It's actually a two-by-two matrix, with nested ones:

\documentclass{article}
\usepackage{amsmath,array}

\begin{document}

\[
U'=\left(
\begin{array}{@{}c|c@{}}
U & \begin{array}{@{}c@{}} a \\ b \\ \vdots \end{array} \\
\cline{1-1}
\multicolumn{1}{@{}c}{
  \begin{matrix} a & b & \cdots \end{matrix}
} & z
\end{array}
\right)
\]

\end{document}

Answer 3

If you like to have more dots without interruption, you may wish to use tikz.

 \documentclass{article}
 \usepackage{amsmath}
 \usepackage{tikz}
 \usetikzlibrary{matrix}
 \begin{document}
 \[U'~=~\left(
 \vcenter{\hbox{\begin{tikzpicture}
 \node[matrix of math nodes] (mymat) {
    &  & ~& \left(U^{(k+1)}_a\right)_{0k} \\
    &  & ~& \left(U^{(k+1)}_a\right)_{1k} \\
    & ~~~~~~{\text{\Huge$U$}}~~~~~~ & &  \\[1cm]
  ~  &  & ~ & ~ \\
 a   &  &  & \left (U^{(k+1)}_a\right)_{kk}\\
 };
 \draw (mymat-1-4.north west) -- (mymat-5-4.north west);
 \draw (mymat-4-1.south west) -- (mymat-4-3.south east);
 \draw[ultra thick,line cap=round,dash pattern=on 0 off 1.6mm](mymat-2-4)--(mymat-4-4);
 \draw[ultra thick,line cap=round,dash pattern=on 0 off 1.6mm](mymat-5-1)--(mymat-5-4);
 \end{tikzpicture}}}\right)
 \]
 \end{document}

Answer 4

With {pNiceArray} of nicematrix. With that environment, the rules specified by \Hline (similar to hline) and the specifier | in the preamble are not drawn in the virtual blocks delimited by the commands for continuous dotted lines (\Vdots and \Cdots).

\documentclass{article}
\usepackage{nicematrix}

\begin{document}

$U' = 
\begin{pNiceArray}{ccc|c}[xdots/shorten=4pt,left-margin=2pt]
\Block{3-3}{U}
  &   &        & a \\
  &   &        & b \\
  &   &        & \Vdots \\
\Hline
a & b & \Cdots & z 
\end{pNiceArray}$

\end{document}

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