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Display information for equation id:math.1446.24 on revision:1446

* Page found: Relativistische Formulierung der Elektrodynamik (eq math.1446.24)

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Ko- und Kontravariante Schreibweise der Relativitätstheorie Eq: math.2169.24

Hash: 6d6bfc9ebe700980b23e887b0c88e5ad

TeX (original user input):

\begin{align}
& \left( \begin{matrix}
{{x}_{0}}\acute{\ }  \\
{{x}_{1}}\acute{\ }  \\
{{x}_{2}}\acute{\ }  \\
{{x}_{3}}\acute{\ }  \\
\end{matrix} \right)=\left( \begin{matrix}
\frac{1}{\sqrt{1-{{\beta }^{2}}}} & \frac{-\beta }{\sqrt{1-{{\beta }^{2}}}} & 0 & 0  \\
\frac{-\beta }{\sqrt{1-{{\beta }^{2}}}} & \frac{1}{\sqrt{1-{{\beta }^{2}}}} & 0 & 0  \\
0 & 0 & 1 & 0  \\
0 & 0 & 0 & 1  \\
\end{matrix} \right)\left( \begin{matrix}
{{x}_{0}}  \\
{{x}_{1}}  \\
{{x}_{2}}  \\
{{x}_{3}}  \\
\end{matrix} \right) \\
& x{{\acute{\ }}^{i}}={{U}^{i}}_{k}{{x}^{k}} \\
\end{align}

TeX (checked):

{\begin{aligned}&\left({\begin{matrix}{{x}_{0}}{\acute {\ }}\\{{x}_{1}}{\acute {\ }}\\{{x}_{2}}{\acute {\ }}\\{{x}_{3}}{\acute {\ }}\\\end{matrix}}\right)=\left({\begin{matrix}{\frac {1}{\sqrt {1-{{\beta }^{2}}}}}&{\frac {-\beta }{\sqrt {1-{{\beta }^{2}}}}}&0&0\\{\frac {-\beta }{\sqrt {1-{{\beta }^{2}}}}}&{\frac {1}{\sqrt {1-{{\beta }^{2}}}}}&0&0\\0&0&1&0\\0&0&0&1\\\end{matrix}}\right)\left({\begin{matrix}{{x}_{0}}\\{{x}_{1}}\\{{x}_{2}}\\{{x}_{3}}\\\end{matrix}}\right)\\&x{{\acute {\ }}^{i}}={{U}^{i}}_{k}{{x}^{k}}\\\end{aligned}}

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MathML (4.612 KB / 540 B) :

\begin{aligned} (\begin{matrix} x_{0} \overset{´}{} \\ x_{1} \overset{´}{} \\ x_{2} \overset{´}{} \\ x_{3} \overset{´}{} \end{matrix}) = (\begin{matrix} \frac{1}{\sqrt{1 - β^{2}}} & \frac{- β}{\sqrt{1 - β^{2}}} & 0 & 0 \\ \frac{- β}{\sqrt{1 - β^{2}}} & \frac{1}{\sqrt{1 - β^{2}}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}) (\begin{matrix} x_{0} \\ x_{1} \\ x_{2} \\ x_{3} \end{matrix}) \\ x {\overset{´}{}}^{i} = {U^{i}}_{k} x^{k} \end{aligned}

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Identifiers

$x_{0}$

$\overset{´}{}$

$x_{1}$

$\overset{´}{}$

$x_{2}$

$\overset{´}{}$

$x_{3}$

$\overset{´}{}$

$β$

$β$

$β$

$β$

$β$

$β$

$x_{0}$

$x_{1}$

$x_{2}$

$x_{3}$

$x$

$\overset{´}{}$

$i$

$U$

$i$

$k$

$x$

$k$

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