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Index notation of matrix tranpose

  1. Oct 13, 2013 #1
    Zee writes in Einstein Gravity in a nutshell page 186

    "let us define the transpose by ##(\Lambda^T)_\sigma^\mu = \Lambda_\sigma^\mu##"

    and even emphasizes the position of the indexes. Yes, they are not exchanged! This must be a typo, right?
  2. jcsd
  3. Oct 13, 2013 #2


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    No, what he says is perfectly fine: he writes ##\Lambda^{\mu}{}{}_{\sigma} = (\Lambda^T)_{\sigma}{}{}^{\mu}## which is not what you wrote above.
  4. Oct 13, 2013 #3
    And you are telling me now that this glitch in the typography of the slightly out of place indexes is the crucial point?:cry:

    Oh my, I thought I understood why we have upper and lower indexes? But what is the meaning of an index slighly shifted to the right?
  5. Oct 13, 2013 #4


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    The left-to-right order of the indices matters: in a matrix representation the first index is the row index and the second index is the column index.

    [tex]A_\lambda{}^\mu = g_{\lambda\nu} \, A^{\nu\mu} = g_{\lambda\nu} \, g^{\mu\sigma} \, A^\nu{}_\sigma[/tex]
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