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Display information for equation id:math.1359.118 on revision:1359
* Page found: Dynamische Systeme und deterministisches Chaos (eq math.1359.118)
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TeX (original user input):
\begin{align}
& \bar{\varpi }{{*}^{(3)}}=\left( \begin{matrix}
0 & 0 & \omega \\
\end{matrix} \right): \\
& 0=\det (A-\lambda 1)=\left| \begin{matrix}
-\lambda & -{{k}_{1}}\omega & 0 \\
{{k}_{2}}\omega & -\lambda & {{0}_{{}}} \\
0 & 0 & -\lambda \\
\end{matrix} \right|=-\lambda \left( {{\lambda }^{2}}+{{k}_{1}}{{k}_{2}}{{\omega }^{2}} \right) \\
& \Rightarrow {{\lambda }_{1}}^{(3)}=0,{{\lambda }_{2/3}}^{(2)}=\pm i\omega \sqrt{{{k}_{1}}{{k}_{2}}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\bar {\varpi }}{{*}^{(3)}}=\left({\begin{matrix}0&0&\omega \\\end{matrix}}\right):\\&0=\det(A-\lambda 1)=\left|{\begin{matrix}-\lambda &-{{k}_{1}}\omega &0\\{{k}_{2}}\omega &-\lambda &{{0}_{}}\\0&0&-\lambda \\\end{matrix}}\right|=-\lambda \left({{\lambda }^{2}}+{{k}_{1}}{{k}_{2}}{{\omega }^{2}}\right)\\&\Rightarrow {{\lambda }_{1}}^{(3)}=0,{{\lambda }_{2/3}}^{(2)}=\pm i\omega {\sqrt {{{k}_{1}}{{k}_{2}}}}\\\end{aligned}}
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