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Display information for equation id:math.1057.4 on revision:1057
* Page found: Vektorraum (eq math.1057.4)
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Hash: 03a3fd12d4c0349b47e5f191659c03c5
TeX (original user input):
\begin{matrix}
\forall \lambda ,\mu \in K,\forall v,w\in {{V}_{M}}: \\
\left( \begin{align}
& \left( \lambda +\mu \right)\centerdot v=\lambda \centerdot v+\mu \centerdot v,\quad \lambda \centerdot \left( v+w \right)=\lambda \centerdot v+\lambda \centerdot w, \\
& \lambda \centerdot \left( \mu \centerdot v \right)=\left( \lambda \centerdot \mu \right)\centerdot v,\quad \text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r }1\in K:1\centerdot v=v \\
\end{align} \right) \\
\end{matrix}
TeX (checked):
{\begin{matrix}\forall \lambda ,\mu \in K,\forall v,w\in {{V}_{M}}:\\\left({\begin{aligned}&\left(\lambda +\mu \right)\centerdot v=\lambda \centerdot v+\mu \centerdot v,\quad \lambda \centerdot \left(v+w\right)=\lambda \centerdot v+\lambda \centerdot w,\\&\lambda \centerdot \left(\mu \centerdot v\right)=\left(\lambda \centerdot \mu \right)\centerdot v,\quad {\text{f }}\!\!{\ddot {\mathrm {u} }}\!\!{\text{ r }}1\in K:1\centerdot v=v\\\end{aligned}}\right)\\\end{matrix}}
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MathML (2.761 KB / 552 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 columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>∈</mo><mi>K</mi><mo>,</mo><mi mathvariant="normal">∀</mi><mi>v</mi><mo>,</mo><mi>w</mi><mo>∈</mo><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></msub><mi>:</mi></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><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="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>λ</mi><mo>+</mo><mi>μ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo variantform="True">⋅</mo><mi>v</mi><mo>=</mo><mi>λ</mi><mo variantform="True">⋅</mo><mi>v</mi><mo>+</mo><mi>μ</mi><mo variantform="True">⋅</mo><mi>v</mi><mo>,</mo><mspace width="1em"></mspace><mi>λ</mi><mo variantform="True">⋅</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>v</mi><mo>+</mo><mi>w</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>λ</mi><mo variantform="True">⋅</mo><mi>v</mi><mo>+</mo><mi>λ</mi><mo variantform="True">⋅</mo><mi>w</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>λ</mi><mo variantform="True">⋅</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>μ</mi><mo variantform="True">⋅</mo><mi>v</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>λ</mi><mo variantform="True">⋅</mo><mi>μ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo variantform="True">⋅</mo><mi>v</mi><mo>,</mo><mspace width="1em"></mspace><mrow data-mjx-texclass="ORD"><mtext>f </mtext></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">u</mi></mrow><mo>¨</mo></mover></mrow></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mtext> r </mtext></mrow><mn>1</mn><mo>∈</mo><mi>K</mi><mi>:</mi><mn>1</mn><mo variantform="True">⋅</mo><mi>v</mi><mo>=</mo><mi>v</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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