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Display information for equation id:math.1058.4 on revision:1058

* Page found: Vektorraum (eq math.1058.4)

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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 (28.187 KB / 2.96 KB) :

∀ λ , μ ∈ K , ∀ v , w ∈ V M : ( ( λ + μ ) ∙ v = λ ∙ v + μ ∙ v , λ ∙ ( v + w ) = λ ∙ v + λ ∙ w , λ ∙ ( μ ∙ v ) = ( λ ∙ μ ) ∙ v , f  ⁢ u ¨ ⁢  r  ⁢ 1 ∈ K : 1 ∙ v = v ) fragments for-all λ , μ K , for-all v , w subscript 𝑉 𝑀 : missing-subexpression formulae-sequence ∙ 𝜆 𝜇 𝑣 ∙ 𝜆 𝑣 ∙ 𝜇 𝑣 ∙ 𝜆 𝑣 𝑤 ∙ 𝜆 𝑣 ∙ 𝜆 𝑤 missing-subexpression : formulae-sequence ∙ 𝜆 ∙ 𝜇 𝑣 ∙ ∙ 𝜆 𝜇 𝑣 f  ¨ u  r  1 𝐾 ∙ 1 𝑣 𝑣 {\displaystyle{\displaystyle\begin{matrix}\forall\lambda,\mu\in K,\forall v,w% \in{{V}_{M}}:\\ \left(\begin{aligned} &\displaystyle\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,\\ &\displaystyle\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) :

∀λ,μ∈K,∀v,w∈VM:((λ+μ)⋅v=λ⋅v+μ⋅v,λ⋅(v+w)=λ⋅v+λ⋅w,λ⋅(μ⋅v)=(λ⋅μ)⋅v,f u¨ r 1∈K:1⋅v=v)

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