![带尺寸的块矩阵方程](https://linux22.com/image/290210/%E5%B8%A6%E5%B0%BA%E5%AF%B8%E7%9A%84%E5%9D%97%E7%9F%A9%E9%98%B5%E6%96%B9%E7%A8%8B.png)
我需要在 LaTex 中写入以下矩阵方程。显示的虚线需要出现在结构中,但不需要有颜色(也可以是黑色)。我在这里使用它只是为了显示所需的对齐。我还需要为各个块指定尺寸,如图所示。最好的方法是什么?
答案1
可以使用 TikZ 和matrix of math nodes
(来自matrix
库)来构建 natrices;尺寸的括号是使用库brace
中的装饰构建的decorations.pathreplacing
:
\documentclass{article}
\usepackage{tikz}
\usepackage{geometry}
\usetikzlibrary{matrix,positioning,decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[
style1/.style={
matrix of math nodes,
every node/.append style={text width=#1,align=center,minimum height=5ex},
nodes in empty cells,
left delimiter=[,
right delimiter=],
},
style2/.style={
matrix of math nodes,
every node/.append style={text width=#1,align=center,minimum height=5ex},
nodes in empty cells,
left delimiter=\lbrace,
right delimiter=\rbrace,
}
]
\matrix[style1=0.65cm] (1mat)
{
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
};
\draw[dashed]
(1mat-3-5.south west) -- (1mat-3-6.south east);
\draw[loosely dashed]
(1mat-5-1.south west) -- (1mat-5-6.south east);
\draw[dash dot]
(1mat-1-4.north east) -- (1mat-8-4.south east);
\draw[]
(1mat-5-2.south east) -- (1mat-8-2.south east);
\node[font=\huge]
at ([xshift=-10pt]1mat-3-3) {$A_{1}$};
\node[font=\Large]
at (1mat-2-5.east) {$0$};
\node[font=\Large]
at (1mat-5-5.north east) {$A_{2}$};
\node[font=\Large]
at (1mat-7-5.east) {$B_{2}$};
\node[font=\Large]
at (1mat-7-1.east) {$0$};
\node[font=\Large]
at (1mat-7-3.east) {$B_{1}$};
\draw[decoration={brace,mirror,raise=12pt},decorate]
(1mat-1-1.north west) --
node[left=15pt] {$n_{1}$}
(1mat-5-1.south west);
\draw[decoration={brace,mirror,raise=12pt},decorate]
(1mat-6-1.north west) --
node[left=15pt] {$n_{2}$}
(1mat-8-1.south west);
\draw[decoration={brace,mirror,raise=5pt},decorate]
(1mat-8-3.south west) --
node[below=7pt] {$n_{2}$}
(1mat-8-4.south east);
\draw[decoration={brace,mirror,raise=5pt},decorate]
(1mat-8-5.south west) --
node[below=7pt] {$n_{2}$}
(1mat-8-6.south east);
\draw[decoration={brace,raise=12pt},decorate]
(1mat-4-6.north east) --
node[right=15pt] {$n_{2}$}
(1mat-5-6.south east);
\draw[decoration={brace,raise=7pt},decorate]
(1mat-1-1.north west) --
node[above=8pt] {$n_{1}$}
(1mat-1-4.north east);
\matrix[style2=1.2cm,right=40pt of 1mat] (2mat)
{
Q_{1} \\
\vdots \\
Q_{n_{1} - n_{2}} \\
\vdots \\
Q_{n_{1}} \\
R_{1} \\
\vdots \\
R_{n_{2}} \\
};
\draw[dashed]
(2mat-3-1.south west) -- (2mat-3-1.south east);
\draw[loosely dashed]
(2mat-5-1.south west) -- (2mat-5-1.south east);
\node at ([xshift=17pt,yshift=-1.2pt]2mat.east) {$=$};
\matrix[style2=0.7cm,right=35pt of 2mat] (3mat)
{
0 \\
\vdots \\
\\
\vdots \\
0 \\
b_{1} \\
\vdots \\
b_{n_{2}} \\
};
\draw[loosely dashed]
(3mat-5-1.south west) -- (3mat-5-1.south east);
\end{tikzpicture}
\end{document}
也许你应该考虑是否有其他方式来显示信息?删除带有尺寸的括号并使用单个虚线样式可以改善结果:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,positioning,decorations.pathreplacing}
\begin{document}
\[
\begin{tikzpicture}[
style1/.style={
matrix of math nodes,
every node/.append style={text width=#1,align=center,minimum height=5ex},
nodes in empty cells,
left delimiter=[,
right delimiter=],
},
style2/.style={
matrix of math nodes,
every node/.append style={text width=#1,align=center,minimum height=5ex},
nodes in empty cells,
left delimiter=\lbrace,
right delimiter=\rbrace,
}
]
\matrix[style1=0.85cm] (1mat)
{
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
};
\draw[dashed]
(1mat-3-5.south west) -- (1mat-3-6.south east);
\draw[dashed]
(1mat-6-1.south west) -- (1mat-6-6.south east);
\draw[dashed]
(1mat-1-4.north east) -- (1mat-9-4.south east);
\draw[dashed]
(1mat-6-2.south east) -- (1mat-9-2.south east);
\node[font=\huge]
at (1mat-3-2.south east) {$A_{1}$};
\node[font=\Large]
at (1mat-2-5.east) {$0$};
\node[font=\Large]
at (1mat-5-5.east) {$A_{2}$};
\node[font=\Large]
at (1mat-8-5.east) {$B_{2}$};
\node[font=\Large]
at (1mat-8-1.east) {$0$};
\node[font=\Large]
at (1mat-8-3.east) {$B_{1}$};
\matrix[style2=1.2cm,right=40pt of 1mat] (2mat)
{
Q_{1} \\
\vdots \\
Q_{n_{1} - n_{2}} \\
Q_{n_{1} - n_{2}+1} \\
\vdots \\
Q_{n_{1}} \\
R_{1} \\
\vdots \\
R_{n_{2}} \\
};
\draw[dashed]
(2mat-3-1.south west) -- (2mat-3-1.south east);
\draw[dashed]
(2mat-6-1.south west) -- (2mat-6-1.south east);
\node at ([xshift=17pt,yshift=-1.2pt]2mat.east) {$=$};
\matrix[style2=0.7cm,right=35pt of 2mat] (3mat)
{
0 \\
\vdots \\
\\
\\
\vdots \\
0 \\
b_{1} \\
\vdots \\
b_{n_{2}} \\
};
\draw[dashed]
(3mat-6-1.south west) -- (3mat-6-1.south east);
\end{tikzpicture}
\]
\end{document}