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 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?
 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 