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TeX (original user input):

\begin{align}
  & {{T}_{\left( \mu \nu  \right)}}\equiv {{S}_{\mu \nu }}:=\frac{1}{2}\left( {{T}_{\mu }}_{\nu }+{{T}_{\nu }}_{\mu } \right)={{S}_{\nu }}_{\mu } \\ 
 & {{T}_{\left[ \mu \nu  \right]}}\equiv {{A}_{\mu }}_{\nu }:=\frac{1}{2}\left( {{T}_{\mu }}_{\nu }-{{T}_{\nu }}_{\mu } \right)={{A}_{\nu }}_{\mu } \\ 
 & {{T}_{\mu }}_{\nu }={{S}_{\mu }}_{\nu }+{{A}_{\mu }}_{\nu } \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{{T}_{\left(\mu \nu \right)}}\equiv {{S}_{\mu \nu }}:={\frac {1}{2}}\left({{T}_{\mu }}_{\nu }+{{T}_{\nu }}_{\mu }\right)={{S}_{\nu }}_{\mu }\\&{{T}_{\left[\mu \nu \right]}}\equiv {{A}_{\mu }}_{\nu }:={\frac {1}{2}}\left({{T}_{\mu }}_{\nu }-{{T}_{\nu }}_{\mu }\right)={{A}_{\nu }}_{\mu }\\&{{T}_{\mu }}_{\nu }={{S}_{\mu }}_{\nu }+{{A}_{\mu }}_{\nu }\\\end{aligned}}

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T(μν)Sμν:=12(Tμν+Tνμ)=SνμT[μν]Aμν:=12(TμνTνμ)=AνμTμν=Sμν+Aμν
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Identifiers

  • T
  • μ
  • ν
  • Sμν
  • Tμν
  • Tνμ
  • Sνμ
  • T
  • μ
  • ν
  • Aμν
  • Tμν
  • Tνμ
  • Aνμ
  • Tμν
  • Sμν
  • Aμν

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