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Display information for equation id:math.1931.38 on revision:1931
* Page found: Räumliche Isotropie (eq math.1931.38)
(force rerendering)Occurrences on the following pages:
Hash: f15f3aef60c6e82211abe1cbc0958872
TeX (original user input):
\begin{align}
& \bar{\bar{M}}=\left( \begin{matrix}
0 & -1 \\
1 & 0 \\
\end{matrix} \right)\Rightarrow {{{\bar{\bar{M}}}}^{2}}=-\bar{\bar{1}},{{{\bar{\bar{M}}}}^{3}}=-\bar{\bar{M}},{{{\bar{\bar{M}}}}^{4}}=\bar{\bar{1}} \\
& {{{\bar{\bar{M}}}}^{2n}}={{\left( -1 \right)}^{n}}\bar{\bar{1}} \\
& {{{\bar{\bar{M}}}}^{(2n+1)}}={{\left( -1 \right)}^{n}}\bar{\bar{M}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\bar {\bar {M}}}=\left({\begin{matrix}0&-1\\1&0\\\end{matrix}}\right)\Rightarrow {{\bar {\bar {M}}}^{2}}=-{\bar {\bar {1}}},{{\bar {\bar {M}}}^{3}}=-{\bar {\bar {M}}},{{\bar {\bar {M}}}^{4}}={\bar {\bar {1}}}\\&{{\bar {\bar {M}}}^{2n}}={{\left(-1\right)}^{n}}{\bar {\bar {1}}}\\&{{\bar {\bar {M}}}^{(2n+1)}}={{\left(-1\right)}^{n}}{\bar {\bar {M}}}\\\end{aligned}}
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MathML (experimentell; keine Bilder) rendering
MathML (4.074 KB / 480 B) :
<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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></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>0</mn></mtd><mtd><mo>−</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>⇒</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mn>1</mn><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mo>,</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mo>,</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mn>1</mn><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>n</mi></mrow></mrow></msup><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mn>1</mn><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>M</mi><mo>¯</mo></mover></mrow></mrow><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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