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final la8

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christian
2019-12-11 16:44:45 +01:00
parent a5ee2063c4
commit 4dec90c98a
2 changed files with 3 additions and 2 deletions
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ws2019/la/uebungen/la8.pdf
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ws2019/la/uebungen/la8.tex
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@@ -330,11 +330,12 @@
ist Basis von $V / \text{ker }(\pi)$. ist Basis von $V / \text{ker }(\pi)$.
Wegen $(u_i)_{i \in I}$ Basis von $U$, folgt also Wegen $(u_i)_{i \in I}$ Basis von $U$, folgt also
$V / \text{ker}(\pi) \stackrel{\sim }{=} U$. $V / \text{ker }(\pi) \stackrel{\sim }{=} U$.
Damit: Damit:
\[ \[
\text{Bild}(\pi) \stackrel{\sim }{=} V / \text{ker }(\pi) \stackrel{\sim }{=} U \text{Bild}(\pi) \stackrel{\sim }{=} V / \text{ker }(\pi) \stackrel{\sim }{=} U
.\] Daraus folgt direkt: .\] Da $U$ das Komplement zu $\text{ker }\pi$ ist, folgt
daraus direkt:
\[ \[
\text{Bild}(\pi) \oplus \text{ker }\pi \stackrel{\sim }{=} U \oplus \text{ker }\pi \text{Bild}(\pi) \oplus \text{ker }\pi \stackrel{\sim }{=} U \oplus \text{ker }\pi
\stackrel{\sim }{=} V \stackrel{\sim }{=} V