Covariant and Contravariant Rank-2 Tensors

1. Jan 4, 2007

Truth Finder

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

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Either to it correctly as required, or to pass it as required.

2. Jan 4, 2007

HallsofIvy

Staff Emeritus
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.

3. Jan 6, 2007

Truth Finder

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.