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Doppelter Inhalt bei Def. 1

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Henry Haustein 2018-07-09 12:24:51 +02:00 • committed by GitHub
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2. Semester/LAAG/TeX_files/Das_Minimalpolynom.tex
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@ -2,7 +2,6 @@
\begin{definition}
Für ein Polynom $P(t)=\sum_{i=0}^n c_it^i\in K[t]$ definieren wir $P(f)=\sum_{i=0}^m c_if^i\in\End_K(V)$, wobei $f^0=\id_V$, $f^1=f$, $f^2=f\circ f$, ...
Für ein Polynom $P(t)=\sum_{i=0}^n c_it^i\in K[t]$ definieren wir $P(f)=\sum_{i=0}^m c_if^i\in\End_K(V)$, wobei $f^0=\id_V$, $f^1=f$, $f^2=f\circ f$, ...
Analog definiert man $P(A)$ für $A\in\Mat_n(K)$.
\end{definition}
@ -103,4 +102,4 @@
\begin{remark}
Der naheliegende "'Beweis"' $\underbrace{\chi_A}_{\in\Mat_n(K)}=\det(t\mathbbm{1}_n-A)(A) =\det(A\mathbbm{1}_n-A)=\det(0)=\underbrace{0}_{\in K}$ ist falsch!
\end{remark}
\end{remark}