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fix: ok
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45gfg9 committed Feb 21, 2024
1 parent 016da6c commit 1ea9abc
Showing 1 changed file with 9 additions and 9 deletions.
18 changes: 9 additions & 9 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 @@ -350,10 +350,10 @@ \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[rotate=45] (0, 6) rectangle (-3, 3) rectangle (-5, 0)
\draw[thick,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)
Expand All @@ -365,7 +365,7 @@ \subsection{实谱定理}
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)
\draw[thick,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)
Expand All @@ -378,11 +378,11 @@ \subsection{实谱定理}
\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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