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PF tensor product space equation

  1. Jan 2, 2010 #1
    In the first equation on this page,

    https://www.physicsforums.com/library.php?do=view_item&itemid=335

    is there a loss of generality when there exists a metric tensor, since in that case

    [tex]V \otimes V \otimes V^* \neq V \otimes V^* \otimes V,[/tex]

    because

    [tex]T^{ij}\;_{k} \neq T^{i}\;_{k}\;^{j}.[/tex]
     
  2. jcsd
  3. Jan 4, 2010 #2

    Fredrik

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    I haven't seen that definition before. It seems weird and awkward compared to the one I'm used to. Also, it says that a vector is a linear function from V to the underlying field, but that would be a covector.
     
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