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 …

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 …

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 …

Nov 5, 2021 · I am having some confusion over the concept of covariant and contravariant vectors. Most text books on tensors define contravariant vectors/tensors as objects whose components vary …

Using this fact we can identify the space of 2-tensors, $V\otimes V$ with the space of linear maps $V\to V$ by sending a pure 2-tensor $a\otimes b$ to the linear map $L_ {ab}$ taking $v\to (v\cdot b) a$ …

Jan 28, 2018 · Both mathematicians and physicists use general tensors, engineers use Cartesian tensors. Most tensors are rank 2 tensors and can be represented by a square matrix.