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Covariant and Contravariant Rank-2 Tensors

  1. Jan 4, 2007 #1
    Dear Fellows,

    Do any one have an idea of whether there must be a system tensor in order to be able to transform from the covariant form of a certain tensor to its contravariant one?

    This is a bit important to get rigid basics about tensors.

    Schwartz Vandslire

    Either to it correctly as required, or to pass it as required.
  2. jcsd
  3. Jan 4, 2007 #2


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    If by "system" tensor you mean "metric" tensor, then yes, in order to have covariant and contravariant vectors and tensors, you must have a metric tensor such that ai= gijaj.

    A more general Riemann space may have a "Riemann connection" rather than a metric tensor but my understanding is that we do no talk about covariant and contravariant vectors and tensors in such a space.
  4. Jan 6, 2007 #3
    Oh! Thanks!

    But, HallsofIvy, let's talk, in special, in Minkoweski Space? I know that the latter is a physical concept, but, it refers to a special case which is 4 indices. What about transforming 4x4-Matrices (or Tensors, to be more precise), not only Vectors?

    But I have a question please. Does the previous relation also apply to transforming position vectors (They are the basics of the coordinate system)?

    What is the meaning of transforming a contravariant tensor to a covariant one?

    Is there more than one type of multiplication WRITTEN IN TENSOR EQUATIONS?

    Schwartz VANDSLIRE.:cool:
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