2

I need to draw the following block matrix

enter image description here

The closest I have got is by using the following code:

\begin{pmatrix}
    \lambda_1 & * & \dots & *\\
    0 &  \lceil &  & \rceil \\
    \vdots  & \mid & A_{n-1} & \mid \\
    0 & \lfloor & & \rfloor 
\end{pmatrix}

which produces enter image description here.

I am open for a tikz based solution; but in that case, it needs to fit properly with the following alignat* environment:

\begin{alignat*}{3}
            A\begin{pmatrix}
            u_1 & \tilde{u}_{2} & \dots & \tilde{u}_{n}
            \end{pmatrix} \quad&=&&\quad    \begin{pmatrix}
            \ lambda_1 u_1 & A\tilde{u}_{2} & \dots & A\tilde{u}_{n}
            \end{pmatrix}\\
            &=&&\quad   \begin{pmatrix}
            u_1 & \tilde{u}_{2} & \dots & \tilde{u}_{n}
            \end{pmatrix}\begin{pmatrix}
                lambda_1 & * & \dots & *\\
                0 &  \lceil &  & \rceil \\
                \vdots  & \mid & A_{n-1} & \mid \\
                0 & \lfloor & & \rfloor 
            \end{pmatrix}
        \end{alignat*}
  • In the first row, I only need \lambda_1, then one asterisk, followed by \dots, followed by another asterisk; as shown in my tried version. – Subhajit Paul Aug 13 '19 at 19:18
3

Two solutions: one based on blkarray, another based on pstricks:

\documentclass{article}
\usepackage{mathtools}
\usepackage{blkarray}
\usepackage{bigdelim}
\usepackage{pst-node, auto-pst-pdf}

\begin{document}

        \begin{alignat*}{3}
        A\begin{pmatrix}
        u_1 & \tilde{u}_{2} & \dots & \tilde{u}_{n}
        \end{pmatrix} \quad&=&&\quad \begin{pmatrix}
        \lambda_1 u_1 & A\tilde{u}_{2} & \dots & A\tilde{u}_{n}
        \end{pmatrix}\\
        &=&&\quad \begin{pmatrix}
        u_1 & \tilde{u}_{2} & \dots & \tilde{u}_{n}
        \end{pmatrix}\begin{pmatrix}
         \begin{blockarray}{@{}cccc@{\;}}
         \lambda_1 & * & \dots & *\\
         \begin{block}{c|@{}ccc@{\;}|}
         \BAhhline{~|---|}
         0 & & & \\
         \vdots & & A_{n-1} & \\
         0 & & & \\
         \end{block}
         \BAhhline{~|---|}
         \end{blockarray}
        \end{pmatrix}
    \end{alignat*}

        \begin{alignat*}{3}
        A\begin{pmatrix}
        u_1 & \tilde{u}_{2} & \dots & \tilde{u}_{n}
        \end{pmatrix} \quad&=&&\quad \begin{pmatrix}
        \lambda_1 u_1 & A\tilde{u}_{2} & \dots & A\tilde{u}_{n}
        \end{pmatrix}\\
        &=&&\quad \begin{pmatrix}
        u_1 & \tilde{u}_{2} & \dots & \tilde{u}_{n}
        \end{pmatrix}\begin{pmatrix}
         \lambda_1 & * & \dots & *\\
         0 & \pnode[-1ex, 2ex]{A} & & \\
         \vdots & & A_{n-1} &\\
         0 & & & \phantom{*}\pnode[0.4ex, -0.4ex]{B}\,\\
        \end{pmatrix}
    \psframe[linewidth=0.4pt](A)(B)
    \end{alignat*}

\end{document} 

enter image description here

0

You can use nicematrix:

\documentclass{article}
\usepackage{mathtools}
\usepackage{nicematrix}
\begin{document}
\begin{alignat*}{3}
A\begin{pmatrix}
u_1 & \tilde{u}_{2} & \dots & \tilde{u}_{n}
\end{pmatrix} \quad
&=&&\quad 
\begin{pmatrix}
\lambda_1 u_1 & A\tilde{u}_{2} & \dots & A\tilde{u}_{n}
\end{pmatrix}\\
&=&&\quad 
\begin{pmatrix}
u_1 & \tilde{u}_{2} & \dots & \tilde{u}_{n}
\end{pmatrix}
\begin{pNiceMatrix}%
[code-after = { \tikz \node [draw, fit = (2-2) ] { } ; },
 extra-right-margin = 1.5mm]
u_1 & \tilde{u}_{2} & \Cdots & \tilde{u}_{n} \\[2mm]
0      & \Block{3-3}{A_{n-1}} & & \\
\Vdots & & & \\
0      & & & \\
\end{pNiceMatrix}
\end{alignat*}
\end{document}

Result of the previous code

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