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Display information for equation id:math.1325.163 on revision:1325
* Page found: Der Hamiltonsche kanonische Formalismus (eq math.1325.163)
(force rerendering)Occurrences on the following pages:
Hash: af1b908482bfe831779799cd14fffb46
TeX (original user input):
\begin{align}
& M=J{{\left( J{{M}^{-1}} \right)}^{T}} \\
& \Rightarrow JM=-{{\left( J{{M}^{-1}} \right)}^{T}}=-{{\left( {{M}^{-1}} \right)}^{T}}{{J}^{T}} \\
& \Rightarrow {{M}^{T}}JM=-{{M}^{T}}{{\left( {{M}^{-1}} \right)}^{T}}{{J}^{T}}=-{{\left( {{M}^{-1}}M \right)}^{T}}{{J}^{T}}=-{{J}^{T}}=J \\
& {{M}^{T}}JM=J \\
\end{align}
TeX (checked):
{\begin{aligned}&M=J{{\left(J{{M}^{-1}}\right)}^{T}}\\&\Rightarrow JM=-{{\left(J{{M}^{-1}}\right)}^{T}}=-{{\left({{M}^{-1}}\right)}^{T}}{{J}^{T}}\\&\Rightarrow {{M}^{T}}JM=-{{M}^{T}}{{\left({{M}^{-1}}\right)}^{T}}{{J}^{T}}=-{{\left({{M}^{-1}}M\right)}^{T}}{{J}^{T}}=-{{J}^{T}}=J\\&{{M}^{T}}JM=J\\\end{aligned}}
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MathML (2.778 KB / 387 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><mi>M</mi><mo>=</mo><mi>J</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>J</mi><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>J</mi><mi>M</mi><mo>=</mo><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>J</mi><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mo>=</mo><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><msup><mi>J</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mi>J</mi><mi>M</mi><mo>=</mo><mo>−</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><msup><mi>J</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mo>=</mo><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mi>M</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><msup><mi>J</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mo>=</mo><mo>−</mo><msup><mi>J</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mo>=</mo><mi>J</mi></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mi>J</mi><mi>M</mi><mo>=</mo><mi>J</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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