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Chap 12. And then there are tensors.
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Joined: 07 May 2009, 16:45
Posts: 62
We have vectors that have components in the form that are scalars for basis of the form Then we have simple q-vectors that have components that are scalars for basis of the form Then we have covectors, or 1-forms with basis and simple p-forms with basis Now we get these tensor things, which we are only given the component form, something like Am I correct in assuming the basis of such an animal is something like ?

Or would it be something like ?

Or some other permutation of vectors and 1-forms?

16 Aug 2009, 05:06 Joined: 26 Mar 2010, 04:39
Posts: 109
No.

Tensors live in a space like this where is a vector space and is its dual. Note that while Grassmann algebras deal with antisymmetric multilinear forms, tensors are just multilinear and in general will split into a symmetric and antisymmetric part.

Once we get to differentiable manifolds then will be the tangent space at a given point on the manifold and will be the corresponding cotangent space. A typical (p,q) basis element will be 16 Apr 2010, 03:55 Page 1 of 1 [ 2 posts ]