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Display information for equation id:math.2653.7 on revision:2653

* Page found: Klein Gordon und Relativität (eq math.2653.7)

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TeX (original user input): 

\begin{align}

& \underline{{{{{x}'}}^{2}}-{{c}^{2}}{{{{t}'}}^{2}}}=\left( \begin{matrix}

{{x}'} & c{t}'  \\

\end{matrix} \right)\left( \begin{matrix}

1 & 0  \\

0 & -1  \\

\end{matrix} \right)\left( \begin{align}

& {{x}'} \\

& c{t}' \\

\end{align} \right)={{\gamma }^{2}}\left( \begin{matrix}

x & ct  \\

\end{matrix} \right)\left( \begin{matrix}

1 & -\beta   \\

-\beta  & 1  \\

\end{matrix} \right)\left( \begin{matrix}

1 & 0  \\

0 & -1  \\

\end{matrix} \right)\left( \begin{matrix}

1 & -\beta   \\

-\beta  & 1  \\

\end{matrix} \right)\left( \begin{align}

& x \\

& ct \\

\end{align} \right) \\

& ={{\gamma }^{2}}\left( \begin{matrix}

x & ct  \\

\end{matrix} \right)\left( \begin{matrix}

1-{{\beta }^{2}} & 0  \\

0 & -1+{{\beta }^{2}}  \\

\end{matrix} \right)\left( \begin{align}

& x \\

& ct \\

\end{align} \right)=\underline{{{x}^{2}}-{{c}^{2}}{{t}^{2}}}

\end{align}

TeX (checked): 

{\begin{aligned}&{\underline {{{{x}'}^{2}}-{{c}^{2}}{{{t}'}^{2}}}}=\left({\begin{matrix}{{x}'}&c{t}'\\\end{matrix}}\right)\left({\begin{matrix}1&0\\0&-1\\\end{matrix}}\right)\left({\begin{aligned}&{{x}'}\\&c{t}'\\\end{aligned}}\right)={{\gamma }^{2}}\left({\begin{matrix}x&ct\\\end{matrix}}\right)\left({\begin{matrix}1&-\beta \\-\beta &1\\\end{matrix}}\right)\left({\begin{matrix}1&0\\0&-1\\\end{matrix}}\right)\left({\begin{matrix}1&-\beta \\-\beta &1\\\end{matrix}}\right)\left({\begin{aligned}&x\\&ct\\\end{aligned}}\right)\\&={{\gamma }^{2}}\left({\begin{matrix}x&ct\\\end{matrix}}\right)\left({\begin{matrix}1-{{\beta }^{2}}&0\\0&-1+{{\beta }^{2}}\\\end{matrix}}\right)\left({\begin{aligned}&x\\&ct\\\end{aligned}}\right)={\underline {{{x}^{2}}-{{c}^{2}}{{t}^{2}}}}\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (57.396 KB / 5.237 KB) :

x ′ 2 - c 2 ⁢ t ′ 2 ¯ = ( x ′ c ⁢ t ′ ) ⁢ ( 1 0 0 - 1 ) ⁢ ( x ′ c ⁢ t ′ ) = γ 2 ⁢ ( x c ⁢ t ) ⁢ ( 1 - β - β 1 ) ⁢ ( 1 0 0 - 1 ) ⁢ ( 1 - β - β 1 ) ⁢ ( x c ⁢ t ) = γ 2 ⁢ ( x c ⁢ t ) ⁢ ( 1 - β 2 0 0 - 1 + β 2 ) ⁢ ( x c ⁢ t ) = x 2 - c 2 ⁢ t 2 ¯ absent ¯ superscript superscript 𝑥 ′ 2 superscript 𝑐 2 superscript superscript 𝑡 ′ 2 superscript 𝑥 ′ 𝑐 superscript 𝑡 ′ absent 1 0 0 1 absent absent superscript 𝑥 ′ absent 𝑐 superscript 𝑡 ′ superscript 𝛾 2 𝑥 𝑐 𝑡 absent 1 𝛽 𝛽 1 absent 1 0 0 1 absent 1 𝛽 𝛽 1 absent absent 𝑥 absent 𝑐 𝑡 absent absent superscript 𝛾 2 𝑥 𝑐 𝑡 absent 1 superscript 𝛽 2 0 0 1 superscript 𝛽 2 absent absent 𝑥 absent 𝑐 𝑡 ¯ superscript 𝑥 2 superscript 𝑐 2 superscript 𝑡 2 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle\underline{{{{{x% }^{\prime}}}^{2}}-{{c}^{2}}{{{{t}^{\prime}}}^{2}}}=\left(\begin{matrix}\par{{x% }^{\prime}}&c{t}^{\prime}\\ \par\end{matrix}\right)\left(\begin{matrix}\par 1&0\\ \par 0&-1\\ \par\end{matrix}\right)\left(\begin{aligned} \par&\displaystyle{{x}^{\prime}}% \\ \par&\displaystyle c{t}^{\prime}\\ \par\end{aligned}\right)={{\gamma}^{2}}\left(\begin{matrix}\par x&ct\\ \par\end{matrix}\right)\left(\begin{matrix}\par 1&-\beta\\ \par-\beta&1\\ \par\end{matrix}\right)\left(\begin{matrix}\par 1&0\\ \par 0&-1\\ \par\end{matrix}\right)\left(\begin{matrix}\par 1&-\beta\\ \par-\beta&1\\ \par\end{matrix}\right)\left(\begin{aligned} \par&\displaystyle x\\ \par&\displaystyle ct\\ \par\end{aligned}\right)\\ \par&\displaystyle={{\gamma}^{2}}\left(\begin{matrix}\par x&ct\\ \par\end{matrix}\right)\left(\begin{matrix}\par 1-{{\beta}^{2}}&0\\ \par 0&-1+{{\beta}^{2}}\\ \par\end{matrix}\right)\left(\begin{aligned} \par&\displaystyle x\\ \par&\displaystyle ct\\ \par\end{aligned}\right)=\underline{{{x}^{2}}-{{c}^{2}}{{t}^{2}}}\par\end{% aligned}}}

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MathML (experimentell; keine Bilder) rendering

MathML (5.893 KB / 527 B) :

x′′2−c2t′′2_=(x′′ct′′)(100−1)(x′′ct′′)=γ2(xct)(1−β−β1)(100−1)(1−β−β1)(xct)=γ2(xct)(1−β200−1+β2)(xct)=x2−c2t2_

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