Some tensors correspond to geometric objects or primitives. As I said, vectors can be thought of as very simple tensors. Some other tensors correspond to planes, volumes, and so on, formed directly from …

Before talking about tensors, one needs to talk about the tensor product of vector spaces. You are probably already familiar with the direct sum of vector spaces. This is an addition operation on …

I want to compute the dimension of the symmetric $k$-tensors. I know that a covariant $k$-tensor $T$ is called symmetric if it is unchanged under permutation of arguments.

The use of indices for tensors originates from notation for matrices and vectors but extends consistently and beautifully first to abstract vector spaces and then to tensors and tensor fields. It should be …

Explore related questions linear-algebra vectors inner-products tensors See similar questions with these tags.

A nice development of tensors in the applied mathematics level can be found in the book "Matrix Analysis for Scientists and Engineers" by Alan Laub. I also like very much the chapter on the tensor …

Finding a basis for symmetric $k$-tensors on $V$ Ask Question Asked 8 years, 8 months ago Modified 1 year, 1 month ago

I've managed to get a weak grip on what the tensor product of two vector spaces is. I'm now trying to understand the tensor product of two algebras. I understand that we define $(v_1\\otimes w_1)(...

May 23, 2019 · Here I will be just posting a simple questions. I know about vectors but now I want to know about tensors. In a physics class I was told that scalars are tensors of rank 0 and vectors are …

I haven't heard of any generalization of determinants to higher-rank tensors, but I cannot offhand think of a principled reason why one couldn't exist. The study of tensors belongs in the field of multilinear …