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, …

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 …

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 …

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 …

Oct 13, 2009 · A tensor is a general quantity. A scalar has magnitude with 0 direction, hence a rank 0 tensor. A vector is a magnitude acting along a line, or 1 dimension, i.e. tensor of rank 1. …

May 11, 2025 · If the curvature tensor is zero then the spacetime is vacuum. If not, then it may not be vacuum (depends on the Einstein tensor). That much is absolutely certain. And FLRW has …