Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Antisymmetric and symmetric part of a general tensor

  1. Mar 7, 2013 #1
    I've seen it stated several times that a general covariant or contravariant tensor of rank n can be separated into it's symmetic and antisymmetric parts

    [tex] T^{\mu_1 \ldots \mu_n} = T^{[\mu_1 \ldots \mu_n]} + T^{(\mu_1 \ldots \mu_n)}[/tex]

    and this is easy to prove for the case n=2, but I don't see how to prove it for a general n. Could anyone help me out?


    (suspect this has been posted in the wrong forum, but I also suspect that the general relativists can answer this question as good or better than the mathematicians)
     
  2. jcsd
  3. Mar 7, 2013 #2

    Bill_K

    User Avatar
    Science Advisor

    You're right, this statement holds only for two indices. For three or more you can separate the totally symmetric part and the totally antisymmetric part, but there's leftovers. This is easy to confirm just by counting up the independent components of the symmetric and antisymmetric parts and seeing that they don't add up to the expected total. We say the leftover part has "mixed" symmetry.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Antisymmetric and symmetric part of a general tensor
  1. Antisymmetric 4-tensor (Replies: 3)

Loading...