What Is a Tensor? The mathematical point of view. - Physics Forums
2024年9月30日 · The tensor product of two 1 dimensional vector spaces is 1 dimensional so it is smaller not bigger than the direct sum. The tensor product tof two 2 dimensional vector spaces …
What, Exactly, Is a Tensor? - Mathematics Stack Exchange
2014年1月30日 · The complete stress tensor, $\sigma$, tells us the total force a surface with unit area facing any direction will experience. Once we fix the direction, we get the traction vector …
An Introduction to Tensors - Mathematics Stack Exchange
A tensor field of type $(0, 0)$ is a smooth function. A tensor field of type $(1, 0)$ is a vector field. A tensor field of type $(0, 1)$ is a differential $1$-form. A tensor field of type $(1, 1)$ is a …
Are there any differences between tensors and multidimensional …
2015年2月5日 · Tensor : Multidimensional array :: Linear transformation : Matrix. The short of it is, tensors and multidimensional arrays are different types of object; the first is a type of function, …
What are the Differences Between a Matrix and a Tensor?
2013年6月6日 · The components of a rank-2 tensor can be written in a matrix. The tensor is not that matrix, because different types of tensors can correspond to the same matrix. The …
abstract-algebra proof-verification modules tensor-products
By universal property of tensor products, this factors through $\mathbb{Z}_m\otimes\mathbb{Z}_n$. Using ...
terminology - What is the history of the term "tensor"?
A part of the tensor history must come from tenses (past present future) and how Aristotle defined time as the measure of change / motion / movement. So really descriptions of changes of the …
abstract algebra - Why is the tensor product important when we …
2011年1月25日 · Tensor products are important in areas of abstract algebra, homological algebra, algebraic topology and algebraic geometry. and tensor products of vector spaces are also …
Definitions for Norm of a Tensor - Mathematics Stack Exchange
2019年2月27日 · The justification is that 'we have estimated the norm of the symmetric tensor $\text{Ric} + \text{Hess}(f)$ in terms of its trace'. I know a bit about matrix norms and norms of …
abstract algebra - What exactly is a tensor product? - Mathematics ...
This is a beginner's question on what exactly is a tensor product, in laymen's term, for a beginner who has just learned basic group theory and basic ring theory. I do understand from wikipedia …