推导这三个矩阵的代码

Question

我想请教一下是否有人能够推导出以下代码：

Answer 1

下面的代码适用于第一个矩阵，因为对于三个矩阵来说它很容易编写。

$\begin{matrix}
& A & \\
& \begin{bmatrix}
        1 & 2 & 3\\
        a & b & c
    \end{bmatrix} &\\
& \mbox{Input matrix} & \\
\end{matrix}$

我在编写此代码时想象该块是一个具有三行的矩阵，其中第二行是另一个矩阵。

Answer 2

和nicematrix：

\documentclass{article}
\usepackage{nicematrix}
\begin{document}
\noindent
$\begin{bNiceMatrix}[first-row,last-row=6]
\Block{1-5}{\text{\small A}} \\
\times & \times & \times & \times & \times\\
\times & \times & \times & \times & \times\\
\times & \times & \times & \times & \times\\
\times & \times & \times & \times & \times\\
\times & \times & \times & \times & \times\\
\rule{0pt}{12pt}
\Block{1-5}{\text{\small Input matrix} }
\end{bNiceMatrix}$
%
\begin{tabular}[c]{c}
$\rightarrow$ \\
\small Phase 1
\end{tabular}
%
$\begin{bNiceMatrix}[first-row,last-row=6]
\Block{1-5}{\text{\small U}}\\
\times & \times & \times & \times & \times\\
\times & \times & \times & \times & \times\\
0 & \times & \times & \times & \times \\
0 & 0 & \times & \times & \times\\
0 & 0 & 0 & \times & \times\\
\rule{0pt}{12pt}
\Block{1-5}{\text{\small Upper Hessenberg}}
\end{bNiceMatrix}$
%
\begin{tabular}[c]{c}
$\rightarrow$ \\
\small Phase 2
\end{tabular} 
%
$\begin{bNiceMatrix}[first-row,last-row=6]
\Block{1-5}{\text{\small T}}\\
\times & \times & \times & \times & \times\\
0 & \times & \times & \times & \times\\
0 & 0 & \times & \times & \times \\
0 & 0 & 0 & \times & \times\\
0 & 0 & 0 & 0 & \times\\
\rule{0pt}{12pt}
\Block{1-5}{\text{\small Upper Triangular}}
\end{bNiceMatrix}$                                                                                     
\end{document}

Answer 3

 \documentclass{article}
 \usepackage{mathtools}
 
 
 \begin{document}
 \noindent{}

 \begin{tabular}{*{5}{c}}
    {\small A}            &                               & {\small U}                &   & {\small T}                \\
    $\begin{bmatrix}
                    \times & \times & \times & \times & \times\\%
                    \times & \times & \times & \times & \times\\%
                    \times & \times & \times & \times & \times \\%
                    \times & \times & \times & \times & \times\\%
                    \times & \times & \times & \times & \times\\%
            \end{bmatrix}
    $                     &
    \begin{tabular}[c]{c}
            $\rightarrow$ \\\small Phase 1
    \end{tabular}
                          & $\begin{bmatrix}
                    \times & \times & \times & \times & \times\\%
                    \times & \times & \times & \times & \times\\%
                    0 & \times & \times & \times & \times \\%
                    0 & 0 & \times & \times & \times\\%
                    0 & 0 & 0 & \times & \times\\%
            \end{bmatrix}  $ & \begin{tabular}[c]{c}
            $\rightarrow$ \\\small Phase 2
    \end{tabular} &
    $\begin{bmatrix}
                    \times & \times & \times & \times & \times\\%
                    0 & \times & \times & \times & \times\\%
                    0 & 0 & \times & \times & \times \\%
                    0 & 0 & 0 & \times & \times\\%
                    0 & 0 & 0 & 0 & \times\\%
            \end{bmatrix}  $                                                                                     \\
    {\small Input matrix} &                               & {\small Upper Hessenberg} &   & {\small Upper Triangular}
 \end{tabular}
 \end{document}