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Display information for equation id:math.1802.48 on revision:1802
* Page found: Kovariante Schreibweise der Relativitätstheorie (eq math.1802.48)
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Hash: 88e9b965047a6433bcccb15e9f485b11
TeX (original user input):
\begin{align}
& {{U}^{i}}_{k}=\left( \begin{matrix}
\gamma & -\beta \gamma & 0 & 0 \\
-\beta \gamma & \gamma & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{matrix} \right)\quad \quad {{U}^{k}}_{l}=\left( \begin{matrix}
\gamma & \beta \gamma & 0 & 0 \\
\beta \gamma & \gamma & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{matrix} \right) \\
& {{U}^{i}}_{k}{{U}^{k}}_{l}=\left( \begin{matrix}
{{\gamma }^{2}}-{{\beta }^{2}}{{\gamma }^{2}} & 0 & 0 & 0 \\
0 & -{{\beta }^{2}}{{\gamma }^{2}}+{{\gamma }^{2}} & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{matrix} \right)=\left( \begin{matrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{matrix} \right)={{\delta }^{i}}_{l} \\
\end{align}
TeX (checked):
{\begin{aligned}&{{U}^{i}}_{k}=\left({\begin{matrix}\gamma &-\beta \gamma &0&0\\-\beta \gamma &\gamma &0&0\\0&0&1&0\\0&0&0&1\\\end{matrix}}\right)\quad \quad {{U}^{k}}_{l}=\left({\begin{matrix}\gamma &\beta \gamma &0&0\\\beta \gamma &\gamma &0&0\\0&0&1&0\\0&0&0&1\\\end{matrix}}\right)\\&{{U}^{i}}_{k}{{U}^{k}}_{l}=\left({\begin{matrix}{{\gamma }^{2}}-{{\beta }^{2}}{{\gamma }^{2}}&0&0&0\\0&-{{\beta }^{2}}{{\gamma }^{2}}+{{\gamma }^{2}}&0&0\\0&0&1&0\\0&0&0&1\\\end{matrix}}\right)=\left({\begin{matrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\\\end{matrix}}\right)={{\delta }^{i}}_{l}\\\end{aligned}}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msub><msup><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>γ</mi></mtd><mtd><mo>−</mo><mi>β</mi><mi>γ</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>−</mo><mi>β</mi><mi>γ</mi></mtd><mtd><mi>γ</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mspace width="1em"></mspace><mspace width="1em"></mspace><msub><msup><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>γ</mi></mtd><mtd><mi>β</mi><mi>γ</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>β</mi><mi>γ</mi></mtd><mtd><mi>γ</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msub><msup><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msub><msup><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mi>β</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>−</mo><msup><mi>β</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msub><msup><mi>δ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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