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minor fixes; fix date

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Niklas Birk 2023-06-09 18:45:26 +02:00
parent 1d1d850672
commit 92a8a61c5f
2 changed files with 2 additions and 2 deletions
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proseminar_skript.tex
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@ -10,7 +10,7 @@
}
\subtitle{TU Bergakademie Freiberg}
\author{Niklas Birk}
\date{16.06.2023 - SS23}
\date{14.06.2023 - SS23}
\addbibresource{proseminar.bib}
\nocite{*}

2
sections/02_berechnung_matrixexponential.tex
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@ -233,7 +233,7 @@ Für $N$ als nilpotente Matrix ergibt sich zudem eine endliche Summe bei der Ber
da ab einem $m \in \NN$ gilt, dass $N^m = N^{m+1} = \dots = 0$, d.h.
\begin{align*}
\e^ {tN } &= \sum^\infty_{k=0} \frac{(t N)^k}{k!}
= \sum^{l-1}_{k=0} \frac{(t N)^k}{k!}
= \sum^{m-1}_{k=0} \frac{(t N)^k}{k!}
= E + t N + \frac{t^2}{2} N^2 + \dots + \frac{t^{m-1}}{(m-1)!} N^{m-1}\\
&= E + t N + \frac{t^2}{2} \begin{pmatrix}
0 & 0 & 1 & & \\