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Question of vocabulary

  1. Aug 14, 2007 #1


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    If a tensor acts on V x V* x V, do we say that it is

    i. 1 time contravariant, 1 time covariant, then 1 time contravariant

    ii. 2 times contravariant, 1 time covariant

    iii. 1 time covariantt, 2 times contravariant

    vi. there is no convention
  2. jcsd
  3. Aug 14, 2007 #2


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    The tensor is neithzer covariant nor contravariant, it's an invariant geometrical object. However, in the canonical basis of the tensor product of spaces under discussion its components are

    [tex] T=T^{i}{}_{j}{}^{k} e_{i}\otimes e^{j}\otimes e_{k} [/tex]

    So which one is it ?i, ii, iii or iv ?
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