Jan 26, 2025 · 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 …

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 …

Jan 30, 2014 · 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 …

Feb 5, 2015 · 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, …

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 …

Jun 6, 2013 · 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 differences …

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 …

May 10, 2007 · A rank 3 tensor inputs three generalized vectors (i.e. either a vector or their dual vector), and spits out a scalar. One can also think of it as inputting 2 generalized vectors (or a …

Jan 11, 2023 · THE METRIC TENSOR. There is a special tensor used often in relativity called the metric tensor, represented by ##g_{\mu \nu}##. This rank-2 tensor essentially describes the …

The amount of memory required to store a tensor grows exponentially with the number of legs, so tensors with lots of legs are usually represented only implicitly: decomposed as operations …