asmodel

Thanks, I suppose I can keep them as separate Tensors but I would combine them in some way. I appreciate your advice.

Well a bi-metric is a good example of what I am doing, its not really a bi-metric, but its similar. I want to represent multiple tensors, that map different spaces, into one tensor.

Here is Bi-metric theory and yes it relates to gravity. http://en.wikipedia.org/wiki/Bimetric_theory

I understand but what if I wanted to describe a bi-metric? For example a bi-metric is where each point is a space N-D is represented by two metric tensors,instead of one. My idea it to represent a bi-metric tensor, with only 1 tensor. Do you see where I am going now?

I understand what a tensor is and what a vector are, and also the relationship they share, and the methods of computing the contra/covariant forms etc. But in a Tensor, even though you can components of a tensor that can be derived from vectors, can a single component of a tensor, itself, be a vector... E.g. a 3-d Tensor, D: Where lambda is itself a 3-D vector?

Is it possible to have a tensor, whereby one or more of its components are themselves vector? This relates to an earlier post.

Hi there thanks, this will work if the vector or tensor is large but if its small it will not work. But perhaps I could use a limit, so that if the vector or tensor satisfies some value then the norm function is applied, otherwise its left intact, but this seems messy and adhoc. Regards.

Looking for an operation that converts a vector or tensor into a scalar, when the vector or tensor value is large. For example, if I multiply a row vector by a column vector, I get a scalar but I really need a function that turns a column vector into a scalar, when its value is significantly large, but if the vectors value is small, the function simply returns another vector. I would like it to work with tensors as well. I hope you find it an interesting problem - I am looking for a function, which can be an operation, but not another vector.