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 …

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 …

Nov 24, 2016 · In an introduction to Tensors it is said that tensors are a generalization of scalars, vectors and matrices: Scalars are 0-order tensors, vectors are 1-order tensors, and matrices are 2 …

Feb 5, 2015 · The short of it is, tensors and multidimensional arrays are different types of object; the first is a type of function, the second is a data structure suitable for representing a tensor in a coordinate …

Jun 5, 2013 · What is the difference between a matrix and a tensor? Or, what makes a tensor, a tensor? I know that a matrix is a table of values, right? But, a tensor?

Jan 15, 2021 · Strictly speaking, tensors of a fixed rank form a vector space (over $\mathbf R$, say), and thus "tensors are vectors" for pure mathematicians who don't work in anything related to physics …

Dec 1, 2022 · Note that the $\I$ in your post actually equals $\G$, which is one of the isotropic tensors but not the identity tensor (although it does yield a scalar multiple of the identity matrix).

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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 …