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docs: fix graph mess
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45gfg9 committed Feb 21, 2024
1 parent 94c1878 commit 016da6c
Showing 1 changed file with 22 additions and 22 deletions.
44 changes: 22 additions & 22 deletions 讲义/专题/22 内积空间上的算子.tex
Original file line number Diff line number Diff line change
Expand Up @@ -350,39 +350,39 @@ \subsection{实谱定理}
\small
\begin{tikzpicture}
\tikzset{->-/.style={decoration={
markings,
mark=at position .6 with {\arrow{stealth}}},postaction={decorate}}}
markings,
mark=at position .6 with {\arrow{stealth}}},postaction={decorate}}}

\draw[thick,rotate=45] (0, 6) rectangle (-3, 3) rectangle (-5, 0)
\draw[rotate=45] (0, 6) rectangle (-3, 3) rectangle (-5, 0)
(-3, 3) rectangle(-3.35, 3.35)
coordinate (xr) at (-2, 4)
coordinate (xn) at (-4, 2)
coordinate (x) at (-2, 2)
coordinate (0n) at (-3, 3);
\node at (-1, 5) {行空间};
\node at (-4, 1) {$A$的核空间};
\node at (-1.5, 6.5) {$\dim r$};
\node at (-4, 4) {$\mathbf{R}^n$};
\node at (-6, 3) {$\dim n-r$};

\draw[thick,rotate=30] (6, 2) rectangle (3.5, -2) rectangle (0, -4)
coordinate (0n) at (-3, 3)
node at (-1, 5) {行空间}
node at (-4, 1) {$A$的核空间}
node at (-1.5, 6.5) {$\dim r$}
node at (-4, 4) {$\mathbf{R}^n$}
node at (-6, 3) {$\dim n-r$};

\draw[rotate=30] (6, 2) rectangle (3.5, -2) rectangle (0, -4)
(3.5, -2) rectangle (3.85, -2.35)
coordinate (b) at (4.5, 0.5)
coordinate (0m) at (3.5, -2);
\node at (5, 1.5) {列空间};
\node at (2, -3) {$A^{\mathrm{T}}$的核空间};
\node at (7, 0) {$\dim r$};
\node at (5, -3) {$\mathbf{R}^m$};
\node at (4, -4.5) {$\dim m-r$};
coordinate (0m) at (3.5, -2)
node at (5, 1.5) {列空间}
node at (2, -3) {$A^{\mathrm{T}}$的核空间}
node at (7, 0) {$\dim r$}
node at (5, -3) {$\mathbf{R}^m$}
node at (4, -4.5) {$\dim m-r$};

\foreach \point in {xr, x, xn, 0n, b, 0m}
\fill[black] (\point) circle (1pt);

\node[left] at (xr) {$x_r$};
\node[below right] at (x) {$x=x_r+x_n$};
\node[left] at (xn) {$x_n$};
\node[right] at (0n) {0};
\node[right] at (b) {$b$};
\node [left] at (xr) {$x_r$};
\node [below right] at (x) {$x=x_r+x_n$};
\node [left] at (xn) {$x_n$};
\node [right] at (0n) {0};
\node [right] at (b) {$b$};

\draw[->-,very thick] (xr) -- node[above,sloped] {$Ax_r = b$} (b);
\draw[->-,very thick] (x) -- node[below,sloped] {$Ax = b$} (b);
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