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Chap 12. And then there are tensors. http://www.roadtoreality.info/viewtopic.php?f=22&t=1416 
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Author:  DimBulb [ 16 Aug 2009, 05:06 ] 
Post subject:  Chap 12. And then there are tensors. 
We have vectors that have components in the form that are scalars for basis of the form Then we have simple qvectors that have components that are scalars for basis of the form Then we have covectors, or 1forms with basis and simple pforms 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 1forms? 
Author:  robin [ 16 Apr 2010, 03:55 ] 
Post subject:  Re: Chap 12. And then there are tensors. 
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 
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