diff --git "a/\350\256\262\344\271\211/\344\270\223\351\242\230/22 \345\206\205\347\247\257\347\251\272\351\227\264\344\270\212\347\232\204\347\256\227\345\255\220.tex" "b/\350\256\262\344\271\211/\344\270\223\351\242\230/22 \345\206\205\347\247\257\347\251\272\351\227\264\344\270\212\347\232\204\347\256\227\345\255\220.tex" index 1e27085..c8f87c5 100644 --- "a/\350\256\262\344\271\211/\344\270\223\351\242\230/22 \345\206\205\347\247\257\347\251\272\351\227\264\344\270\212\347\232\204\347\256\227\345\255\220.tex" +++ "b/\350\256\262\344\271\211/\344\270\223\351\242\230/22 \345\206\205\347\247\257\347\251\272\351\227\264\344\270\212\347\232\204\347\256\227\345\255\220.tex" @@ -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);